Rejecting someone because a core group of players are not compatible is not a bad thing. A individual who will cause more people to opt out of a concept or cause friction among them is a textbook problematic player and it should not be a taboo to reject them. This isn’t something I’ve had to deal with in GMing, but others I know, and I find it kind of absurd that someone would assert that they should be allowed to be given a chance despite several accepted players already feeling uncomfortable and debating opting out if their acceptance is greenlit. At a certain point you need to, as a GM, wage the pros and cons in that situation, and ask themselves “is this person worth the possibility of derailing my role-play?”. It is a good bias to have to void acceptance of someone if you are going to lose your committed player pool. 

Do not accept problematic, toxic, or otherwise conflictive players. Especially if your current pool shares a majority of opinion of them not being compatible. Protect your committed players if it is [i]actually[/i] a problem.