It's not so much the honour or loyalty aspects of Westerns - I still regard those as valuable, though that may be an old-fashioned view nowadays - but more the predictability of some plots and the stodginess of some dialogue, not to mention the stereotyping of some characters. The technical aspects of some old Westerns can be off-putting, too.
A film like "Hombre", which was based on an Elmore Leonard story, did question some of the stereotyping, though I recall it had little dialogue and was a bit too slow-moving at times. It has an exquisite, existential moment. The "baddie", at the end of a truce or ceasefire in which he offers to trade a hostage for money, asks if there are any questions. The "hero" (maybe not the right word in this instance) replies, "How are you going to get back down the hill?", as he lifts his rifle. In the film it's a sort of clash of cultures.