Well, I already bought the books, so I will read them. I may tell you my experience after that.
Now, on the topic: I used to have a ban on evil-PCs, but right now I'm thinking about removing it. Not sure how that will go, but some players truly wanted to play one; what could possibly go wrong, after all?
You'll be fine. Alignment means less in 5e than in prior editions.
Focus more on table ettiquette and what kind of game you all want to play.
If players take alignment seriously and try to play to their alignment, then you may want to limit to Lawful or Neutral Evil.
If anyone plays a CE character true to character, it will just make for an awful game in my experience. Actually, ANY chaotic character. CG can be just as annoying. I'm more inclined to say no CHAOTIC characters than no EVIL characters.
In my current campaign, I allowed a player that joined the campaign many months after it started to play a Yuanti Pureblood. It was originally an NPC that the party helped escape from a prison as she promised that they would be rewarded if they returned her to her people. We turned that NPC into a PC and fleshed out a background that would make sense for the campaign. It has worked out well.
I don't want to get to philosophical, but one can be evil and still be loyal. You are not going to trust a psychopath to look out for your best interests, but you can do business with him. In fact, you likely have worked with or for people with psychopathic character traits. Psychopaths (as opposed to sociopaths) can (and do) function very well in lawful societies.
Devils in fantasy exemplify this. IRL history, the Natzis are the go-to example of LE.
Talk to the player(s) about what makes their character LE? Are they psychopaths who have little to no empathy and see others as means to an end or obstacles to be destroyed? Or instead of psychopaths, perhaps they have incredible love for their own people, nation, organization, or ideal?
Some LE character types that can work even in mostly Good parties:
1. The Psycopath--using party for his goals. He is in this for his own ends. Other party members very well may not realize that he is "evil" or a psychopath. He could be the most liked member or leader of the party. Likely very charismatic.
2. The psychopath--narcissist. Like #1, but may believe that he is working for a greater goal than himself, but finds himself the most important person for realizing that goal. Is incredibly gracious when you are on his good side, but cannot take criticism. "You are either with me or against me and if you don't agree with me, you must be against me."
3. The racist/fascist/ethnocentric/___-ist. This is someone who may seem like a great, generous, kind, and loving person...to her own group. But she harbor great hate for a specific group--or--feels that her group is supior over all others. What makes this person evil is that she sees the hated group, or those outside her favored group, as subhuman. Will defend slavery, ethnic cleansing, genocide, etc. You have to be careful allowing these kinds of characters and make sure that other players in the group are okay with this. This doesn't mean that the character can get away with acting on her beliefs, or that she has to constantly act out hate speech, but even when acting this kind of character in a fantasy world (I hate all beast people, etc.), it can hit too close to home for some players.
4. The greedy or silf-indulgent/addicted--the murder hobo. Greed and addition are forms of self indulgence that when taken to extreme can make you evil. Actually I would say that many PC that don't have Evil written down on their character sheets act evil in the sense of being murder hobos. These characters can work well and be fun to play, because while they don't have any qualms wiping out a lair of kobolds for gold, they can just shrug their shoulders and say "whatever" if the other party members say to spare the children or those who surrender. These characters can be very loyal to their friends, but their circle of ethics is very small.