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I run a game with around 6 people. One of my players (A) wants another one of my players (B) not to play with us anymore.

A has come to me in the past two different times with complaints about B, saying that B's being really disruptive during the sessions (which he was) and that he was saying offensive things/putting offensive memes in the group chat. I talked to B about it and he said that he'd work on it. This was about a month or so ago.

Just now, A has texted me saying that B has now posted some white supremacist stuff in that group chat and that he doesn't feel safe playing with B anymore and that he thinks we should should stop playing with him.

Should I ask the other group members what they think (which would be completely biased, since two of the other members were B's friends before we started playing) or should I just ask B to leave?

The purpose of a tabletop RPG is to be an interactive social experience where all parties involved can enjoy themselves. If at any point this is not happening then it has stopped being a fruitful and worthwhile experience.

In most situations where someones enjoyment was being infringed upon I would council weighing their concerns and discussing it with all parties involved in order to come to an amicable agreement that allowed everyone to continue enjoying themselves, or at least allowed the most people to continue doing so. However, this is not a normal situation. If player B has continued to post offensive content after being warned about it then that is already a repeat infraction.

If the offensive content is indeed white supremacist material then it bridges into something entirely different, no longer just a source of discomfort but indeed a source of real danger and dread for your other players. I do not know Player A's situation, whether they are a POC, a woman, a religious minority, lgbt, or if they are just a white straight Christian dude who is uncomfortable with bigotry, but the very nature of white supremacy is antithetical to the environment of TTRPG because it is inherently dangerous to everyone.

Of course ask to see the group chats and verify if what they say is going on, but also be prepared to act on it if and when it is true, and also if you feel it isn't white supremacist ask Player A to tell you why they think it is, and then address the situation with player B to see their response. Player B's reaction might tell you everything that you need, but don't ever tell them it was Player A that pointed it out, for their own safety.

Ask to see the group chat posts before you make your decision. Evidence is hard to argue with, and seeing as you’ve had to talk to B before about offensive content, it would be harder for them to claim it’s a joke.

If A is correct and he is posting these sorts of things, it may be best to let B go. Otherwise, you are likely going to lose player A if they don’t feel safe playing at your table. Better to lose the troublemaker and avoid being tarred with the same brush as them.

You said player B has posted white supremacist stuff in the group chat (a forum that aught to have some sort of logging on conversations that you can review), so frankly this isn't about group dynamics anymore or how the other players at the table might feel, this is about whether or not you want to implicitly condone racism, because allowing player B to remain will absolutely send that message.