About the gay thing, there were definitely gay clubs in London at the time & quite widely known about, only question is whether York was too provincial.
Though illegal there was also far less of a moral panic about homosexuality in the '20s than there was to be later: Yes, it was illegal and punishments quite harsh, but on the whole people were probably less likely to look for it and report it. The 40s/50s was when it got really nasty, not least because it was tied up with fears of traitors and spies. And even then, people did overlook it if it served their interests. There is a story that the Queen Mother was approached by the Secret Service and asked to get rid of any homosexual staff due to risks of blackmail. Her response was, "We'd have to go into self-service then" . But that was much later than the 20s.
Nobody wanted to TALK about it much in the 20s, certainly not recognise it as equal to heterosexuality, but at a time when trained servants are getting rare, why would you risk losing a trained butler, who knows and accepts the ways of the house, when he isn't actually causing any scandal? Barrow leaves the hallboys alone (the family might reflect that unlike so many of his fellow butlers he is unlikely to be getting the maids pregnant), he is also sober (again unlike many of his fellow butlers) and seems willing to accept a very modest lifestyle for his rank. From the pov of the Crawley he really has a lot going for him.
A real life butler would be expecting a proper cooked breakfast, 3 course dinner served on a proper tablecloth in a separate room for upper servants, not slumming it with maids and hall boys, and decent wine with his meals and port afterwards. He would be the one in charge of hirings and firings, not the one who comes in one day to find that somebody else is at his desk and he can just hang around and take orders and be referred to as Something or other. Which is why Mary's behaviour is so unacceptable here. Yes, the door slamming was childish (and typical of Barrow) but Mary's impulsive action, just barging in without any thought of etiquette was equally immature. They're as childish as one another those two. But at the same time, nobody at the time would have expected the butler to accept being spoken to like some junior kitchen maid, that just wasn't how these things worked.
There was also less of a tendency to think of homosexuality as defining personality and not just illegal acts,. As Barrow points out it series 3 it is the acts that are illegal. For the rest, people were aware of Feminine Men, but the concept "gay" hadn't been invented. As long as he doesn't look very feminine (in which case he might have got a job as a valet but hardly as a butler where an imposing exterior mattered), and doesn't get caught in illegal acts, then as far as the 1920s go, there probably isn't much to think about. The upper servants get edgy when he does seem to show an interest in someone, but otherwise they probably don't think about it. It's not an era where people talk about their sexuality much anyway.