The whole goal of Blockchain is that people - especially people who don't trust each other - can share valuable data in a safe way, without tampering. That's because blockchains store data using sophisticated mathematical innovative software rules that are extremely difficult for hackers to manipulate.
But even the best-designed blockchain systems can sometimes fail in the area of security in places where fancy math and software rules come into contact with people - who are adept cheaters - in the real world. To understand why, I have to start by explaining what makes blockchains - in principle - "safe". Bitcoin (there you have it again) is a good example of this. In Bitcoin blockchains, the shared data is the history of every Bitcoin transaction ever made: a ledger. This ledger is stored in multiple copies on a network of computers, these are called "nodes". Every time someone sends a transaction to the general ledger, it is checked with the nodes. Some of them (Bitcoin owners) compete to wrap valid transactions in "blocks" and add them to a range of other transactions. The owners of these nodes are referred to as "miners". Miners - miners - who successfully add new blocks to the chain earn bitcoins as a reward. What makes this system theoretically impossible to manipulate are two things: a cryptographic fingerprint unique to each block and a "consensus protocol", the process which the nodes in the network correspond to a shared history.
The fingerprint, called a hash, takes a lot of time and energy to generate initially. So it serves as proof that the miner who added the block to the blockchain did the computational work to earn a bitcoin reward (for this reason Bitcoin would use a "proof-of-work" protocol). It also serves as a kind of seal, since changing the block should generate a new hash. Checking whether the hash matches the block is easy, however, and once the nodes have done that, they update their respective copies of the blockchain with the new block. This is the consensus protocol. The final security element is that the hashes also serve as the links in the blockchain: each block contains the unique hash of the previous block. So if you want to retroactively change an entry in the ledger, you need to calculate a new hash not only for the block it is in, but also for each subsequent block. And you need to do this faster than the other nodes can add new blocks to the chain. So unless you have computers that are more powerful than the rest of the nodes combined (and even then success is not guaranteed), any blocks you add will conflict with existing blocks, and the other nodes will automatically reject your changes. This is what makes the blockchain "mess-free" or "unchanging".
So much for the theory because implementation in practice is more difficult. The simple fact that a system works like Bitcoin - as many cryptocurrencies do - does not mean that it is just as secure. Even when developers use proven and cryptographic tools, it's easy to accidentally bring them together in ways that aren't safe. Bitcoin has been the longest, so it has been most thoroughly tested. One possibility is an eclipse attack. Nodes on the blockchain must remain in constant communication in order to compare data. An attacker who succeeds in taking control of a node's communication and misleading it into accepting fake data that appears to come from the rest of the network can mislead it by wasting resources or making fake transactions.
In the end 'safe' is very difficult to define in the context of blockchains. It all depends on your perspective.