One player, a couple of months ago, had a problem about a ruling I made in a tier 1 game. It was a minor ruling in which I gave an npc wizard in a carriage a +2 AC bonus for 1/2 cover. She argued with me, I maintained the ruling, she continued to argue, I tried to move on, and I eventually said "The wizard is dead," I removed the wizard from the game map, and went on to the next player in initiative order. This resulted in the player leaving, and contacting Adventurers League managers at WotC.
She added an additional complaint that I was not calling her by the correct pronoun, as she is transgender. Having had transgender friends in the past, I am used to such people telling me the pronoun they prefer. She never told me, however, and as I recall I called her 'she' consistently.
It was later determined not only that I have control over rules at my table, but also that my ruling was fair and accurate to the module. Additionally, it was determined there was no malice in my pronoun usage, and any mistake was accidental.
However the fallout resulted in a mutual decision we would not play at the same table anymore. This is completely fine with me: the way I look at it, I am not going to play with a DM I don't want to play with either, no big deal. There are other tables, and other DM's. It seemed this was the agreed resolution between me, her, and the coordinator.
However, I just tried to run a tier 3 game. This individual signed up. Rather then apologizing, she said "I talked to some people, and I can play at your table if I have another DM playing with me to contest your rulings." At first, I thought she was apologizing; now I realize she was strengthening her bullying position. As it turns out, the rest of the people who signed up decided to play other games, because they didn't want to play at the same table with her. She has a reputation as a cheater and a bully. I got text messages from players later indicating this is what happened. So the module I had prepared was wasted, as was my time, as we did not have enough players.
As a DM in Adventurers League, can I forbid a player from playing at my table, or is this up to the public venue in which the event is held, or something else?