As far as the writing contest is concerned, I have no issue with it saying "no LGBTQ theme". To me this is talking about the genre, in the same way that it says "no horror", "no sci fi", "no romance", "no erotica" and is banning pretty much everything in the planet. From writing contests I have seen, they usually go the other way, saying that it must be on this theme, as opposed to banning things. I really think it's a stretch to suggest it is bigoted based purely on that. They do allow gay characters, just not LGBTQ theme. It's probably redundant since they've already banned romance and erotica and since LGBTQ theme is going to be either romance or erotica, and they could have worded it better.
QUILTBAG/LGBTQ does not mean romance and erotica. This is the problem. It's the assumption that everyone who falls somewhere in the QUILTBAG/LGBTQ area is inherently sexual. It's this attitude that it used to object to QUILTBAG people in children's media, regardless of the context, because simply existing in the story is seen as a sexual act. This is the first sign that it's based on bigotry, because the connection was drawn that banning anything QUILTBAG/LGBTQ was equivalent to banning sexual content.
When a person tries to soften it by saying they might consider some characters at their discretion, this is an attempt to get out of criticism. But it doesn't remove the problem. They're coming from a place of viewing those characters as abnormal and something that shouldn't be there. The stories they'll take at their discretion would be ones that uphold bigotry. In other words, the "LGBTQ theme" is any story that has a positive portrayal. It's not a genre and it's not equivalent to banning a genre.
Another red flag is there's a blog post by the person running the contest saying that discrimination isn't bad. Then using a lot of examples that carefully avoid any identity-based discrimination, like trying to avoid scams. But you know what's being talked about, because the main use of discrimination is to talk about bigotry. This is another common tactic to avoid direct criticism, by using an example that isn't the contentious one, when it's clear what is actually being discussed.
There was a similar thing with a short fiction market, where one of the editors turned out to be anti-QUILTBAG. When this came out, he instead talked about stories tackling gun control, and said it'd be about whether the story normalised gun control or not. He wasn't really talking about gun control. He was talking about whether stories normalised things like gay marriage or whether they showed such things as terrible. He wanted stories that were the latter. So, yes, he would actually have taken stories with gay characters, but in a way that was not any less bigoted.
In short, bigots are very good at coming at it from around the houses, in a way that it is clear what they mean to the targets who've been here many times before... but they can argue they didn't directly say it.