There are anti-Saudi demonstrations at every home game, though not well attended. Those protesting are largely left in peace by the rest of the fans, which is a scintilla of relief.Hmm. Hopefully we'll never find out, but I'm not so sure. What were/are the scale of the protests at Newcastle? Are there still massed demonstrations against the ownership? (Indeed were there any?)
I think football fans are football fans and ultimately as people we're no more holy and righteous than the Geordies. I'm not (really) denigrating our fanbase, because I'm sure we would protest, and more vehemently than the Newcastle fans, but I don't think that would be because we're morally superior, more that because at Newcastle the Saudis took over from an extremely unpopular owner, whereas any change of ownership at Brighton will mean replacing a man most of us regard as almost a living saint. Ultimately though I think those who mumble "I just wanna watch football and see my team do well" will win.
Anyway, like I say, all hypothetical and I hope we NEVER have to find out how we'd behave.
You're absolutely right that resistance to the new owners would be stronger had they taken control from a well-liked owner (or one that wasn't actively and vehemently loathed). We'd protested in large number against Ashley's ownership with; banners, marches, disruption and eventually boycotts. To absolutely no avail. Ashley wasn't truly keen on selling until his excessive valuation was met by the Saudis. Nothing we had done moved him any closer to selling up than he was a year after buying us, (in fact Mansour courted Newcastle in 2008 prior to his purchase of Man City and Ashley could have sold us back then had he not made a mess of negotiations) so the appetite for protest has been somewhat diminished anyway. I'm sure if results, and poor management were to return that appetite would grow. But I'm sorry to say that as it stands, because a well liked manager is getting well liked players to produce well liked style of pretty successful football, the atrocities committed by our owners don't take up the kind of room in the discourse as they should.
You're also right that while it's easy to claim that one would give up their ticket, or protest the sale of Brighton to someone similar, until it actually happens it's impossible to say what they'd do. The Newcastle fanbase isn't some sort of cohesive hivemind. We all have our own reasons for going to the match and supporting the club. For some it's familial tradition, some it's geography, for others from further afield it's a random choice of PL clubs, but each has their very singular reason for supporting the club. Like you say, many don't care about what happens away from the pitch. For many others it's an uncomfortable circle to square; how do I support the club I've supported all my life, and show my displeasure at who now owns it? For others it's a bridge too far and they've begrudgingly walked away.
There's unfortunately a trend in football that any perceived attack on any facet of a club, is met with outrage and whataboutery and all that nonsense. I know I've been guilty of reading some stuff by fans of other clubs, about Newcastle fans being morally bankrupt and the like, and taking it as an attack. Some of it is just usual partisan football 'banter', some of it comes from a pretty narrow minded view, but some of it is legitimate criticism.