A Bitcoin Tumblr link is supposed to clear out your old address to make room for a new one. Since Bitcoin is not regulated (in any way) It is meant to confuse and disguise where the Bitcoin is coming from. It is done in such a random fashion.
That means you could be receiving stolen Bitcoin money and not know it. The addresses are concealed during each transaction. Now, there is no law against using a Bitcoin tumblr. You can even use it to buy some virtual private network services, providing it accepts Bitcoin.
The Tumblr Disconnects from the E-Wallet
Let's begin with an example. Say that Henry sends some Bitcoin to Joey. Joey sends some to Susan. Susan then sends some onto Chad. Keep in mind that there is clear blockchain link between Henry and Chad.
However, let's say that Hnery sends something to Joey and then to Susan using the tumblr. The original links and addresses have been removed. There is no way to know who sent what to whom, only when.
The bottom line is that this tunblr creates a clean block. You still get the same money (even if some of it was given out stolen) but the names and links are cleaned out.
Some tumblrs have even go so far as to clear out the identities further by sending out different sizes to different locations.
Is This Illegal?
This is where the "rub" comes in to play. Can you mix the Bitcoins you send to protect your privacy more?
It is good for cashing out cryptocurrency that you might have gotten through ill-gotten gains. There is nothing on the books that say it is illegal. However, there is a great risk if some of your crypto money gets tied up in some dirt money-laundering thing. Just something to keep in mind.
For more information, see bitcoin tumbler.