The short answer? Yes and no, but mostly no.

It all comes down to those pesky, invasive KYC laws.
When Bitcoin was created in 2008 as a response to the financial crisis of the time, it was meant to deliver people from the manipulative and greedy tactics of big banks and government. And it succeeded. But much like comparing the internet from its infancy to now, Bitcoin and the world around it have changed quite a bit.

Credit Cards of The Future

Do you have an account with a popular crypto exchange? A Coinbase, Blockfi, KuCoin, Binance, or Celsius account? Chances are you do, the vast majority of crypto traders do (when writing this the top 10 crypto exchanges had a 24 volume over $27 billion). This means the vast majority of actions and transactions taken by individuals in crypto are about as private as your social media account. Which is to say: they are not private at all.
These massive exchanges operate just like credit cards, monitoring literally every purchase, trade, move, or transaction that takes place in your account. But they don't just monitor your account, they monitor everything, and with the help of third parties who know the value of such data, the digital dossier they build on you is frighteningly detailed.
They monitor not just wallets associated with your account, but any wallet you've ever sent crypto to from that account. They get data from where you shop, where you live, your income, your credit score, your job, your political affiliation--everything. To them, keeping track of your Bitcoin holdings is only one of a litany of data points they keep about you.

If you're a Blockfi member, here is all the data collected just in relation to your finances:

"Transaction Data such as cryptocurrency wallet address(es), information relating to your BlockFi account and cryptocurrency trading transactions and related information for deposits or withdrawals, credit card information (last four digits of number, expiration date, card status), credit card payment information (amount, date, frequency, status, balance), information relating to credit card transactions;
Financial Data such as bank name, bank account number, bank routing number, income type, annual income amount, monthly housing expenses, information that may be received from consumer reporting agencies (e.g., credit bureau reports)."

Knock, Knock. Who's there? Third Parties.

The part where they share your financial information with outside, third parties is what makes me pump the brakes.
Are you someone who stakes and lends out crypto on Celsius? Are you aware they share your details and information with a plethora of other companies?

"Subsidiaries, affiliated companies, subcontractors and other third-party service providers, business partners (such as GEM, Coinify, Simplex and Wyre), auditors or advisers, "any potential purchasers or third party acquirer(s) of all or any portion of our business or assets, or investors in the company."

That is some broad language right there. "Any potential purchasers or third party acquirer of all or any portion of our business or assets, or investors in the company." So they can share your info with their investors if they want, for some odd reason. Not to mention "subsidiaries [and] affiliated companies" could really mean anyone. How does a company become officially affiliated anyways? It matters little when Crypto.com, Coinbase, Kraken, Gemini, and FTX all share your info with "affiliates and subsidiaries."

Why Your Crypto Wallet Probably Isn't Private

Fear. That's the main reason why governments, banks, and the powers that be want to keep an eye on what you're doing in the crypto community, but let me back up and break it down. Let's use the internet as an example again.
When the internet first came out, it was free intelligence. Knowledge abounding. It was a virtual library where anyone could hop on and talk to virtually anyone else. You could share information and research any topic and just learn, at your own pace and in your own way.
But very quickly legislatures and politicians around the world noticed people learning all sorts of things, things that helped them become more powerful, things that our leaders had lied about, things our governments wanted to be kept quiet, things that helped individuals and citizens break out of the societal control they'd been under. It became a potential problem for the herders of humanity. So, those politicians and leaders got their grubby little fingers involved. They started blocking some knowledge and limiting others. They labeled information as "dangerous" and censored subjects that threatened their power. In places where they can't outright prevent your internet access, they heavily monitor it, and put you into categories based on your preference and browsing history, to better keep an eye on you.
Traditionally this level of scrutiny has led to nothing more than retailers and advertisers knowing exactly what to market to you, where, and when. But there are oppressive and authoritarian governments out there who have used this monitorization to oppress, terrorize, and subjugate their people.
Knowledge is power, and knowing what you spend your time reading, watching, and interacting with is a form of power to someone.
And now, Bitcoin.
Just like the internet in its early stages, we are enjoying this newfound power and the freedom it brings to our lives. But just as our leaders got nervous during the meteoric rise of the internet, they are just as anxious now watching crypto. They know this technology has the ability to shift the power dynamic, they know we are freer because of it, they know this technology threatens the corrupt house of cards they've been building for decades at least.
And they are scared.
Look around the worldwide crypto community and you will see the manifestation of that fear abound. India banned all cryptocurrency until they could get ahead of the technology, reign it in, produce their own digital rupee, and gain a portion of every crypto transaction taking place in their country. China banned all cryptocurrencies until they can do the same thing, rolling out their digital yuan. The UK, France, and Germany are all dragging their feet, and depending on who you ask in America you could get very different answers; Republicans want to ban all crypto, Democrats want to allow it/Democrats want to ban all crypto, Republicans want to allow it.
That's not to say every single form of government is scared, of course, when you have states like Arizona and countries like El Salvador representing the crypto community in spades. But for the big guys, the largest stakeholders in the traditional financial system, they're nervously wringing their hands.
Governments are scared. They want to know more about what's happening in this space. How do they do that? They just monitor everything you do.
And with companies like Chainalysis popping up and gaining lots of backers, your privacy is going to get even more assaulted.

So, What Bitcoin Is Private?

If you want to keep your crypto finances private, and we're talking political activist levels of private where your identity, career, and possibly life is on the line, then, just like with the internet--and real-life-- it's all about Peer 2 Peer. P2P allows transacting with another person, minus the ever-watching exchange, which grants both parties anonymity. Places like Hodlhodl.com or Paxful.com are your best bet at finding a large number of buyers and sellers at any given time across the entire world. You may lose some convenience of the large exchanges, like being able to buy whatever you want whenever you want. But for those that desire to be truly private, it's a negligent cost.
The old saying, 'not your keys, not your coins' still holds true. If you don't own the private keys to your holdings, if you're letting a custodian manage your crypto, then you don't have privacy. Full stop. Therefore, you're going to need your own wallet and keys. According to the Bitcoiner Privacy Guide, some of the best wallets to choose from are Samurai Wallet, Bluewallet, and Sparrow Wallet. You'll need one in order to operate on P2P platforms like Paxful.
Once you've acquired your crypto, it's simply a matter of keeping it private, and if you've used something like Samurai Wallet, then you're in good hands. You can even make P2P payments via the Samurai Wallet, staying off the radar while paying your bills.
Bitcoin is blockchain, and blockchain is inherently public. It's visible to anyone, though they may not understand what they're seeing. And the company I mentioned earlier, Chainalysis, is perfecting the art of reading blockchains even when developers may not want them to. They have some powerful clients who need to know what people are buying, with what, how long they are holding it, and when they are selling it in order to make the perfect market moves for the foreseeable future.
Bitcoin's newest upgrade, Taproot, makes some changes to the readability of the blockchain that will help privacy in several key areas, but in order for people to enjoy that upgrade, wallets and exchanges will have to update their software. And as of right now, despite the upgrade being released in November of last year, virtually no one is using it.

In The End...

Do you even care? Does it even matter to you? We have all given our identity and loads of other information freely to credit cards, banks, and social media companies in a short span of time. Do you, the reader, care if your crypto is entirely yours and off the radar versus if it's sitting on a flashy, popular coin exchange? When free crypto and staking rewards are thrown in for using the exchanges, it becomes even harder for people to resist. "Who cares if I have to give up some information, I'm making 59% back on my Polygon!" C'est possible.
What do you think? Are you a private crypto holder or public crypto holder? Do you use P2P or a big exchange? I'd love to know to get a better idea of the current crypto community.