It depends if it's a principled stance or not. For example, loads of them aren't shy about working at HM's Passport Office or the Home Office in Liverpool. The city is packed with public sector jobs all operating under the 'HM' banner, because they are incapable of/unwilling to try to get private enterprise off the ground. If they hated the establishment that much then why would they happily work for the establishment?
Another thing you've got is that they've been to Wembley finals many times between the 1980s and the Klopp era and NOT booed the national anthem. It seemed to come back into fashion once they'd won the 2019 Champions League for no obvious reason other than to say "we're relevant again, how can we make ourselves the centre of attention?".
You look at crowd shots of their end and it's a diverse mix of people, most of whom probably have no connection to the city. They have fewer than 6,000 season ticket holders with a Liverpool postcode. They booed Abide With Me even though the club re-released it to mark the 33rd anniversary of Hillsborough just the other week. That's how stupid, ignorant and uninformed they are.
I could go on about respect and the ever-diminishing quality of being able to disagree with something without being a fucking wanker about it, but that'd take too long. No doubt there are many City fans who are republicans but don't boo it because they are aware that the person next to them might wish to observe it. Not everything is about me, me, me.
In my opinion therefore, booing Abide With Me and the national anthem had fuck all to do with a principled stance and everything to do with a narcissistic cult of self-centred weirdos setting out to make it all about them. Politics doesn't even begin to enter the discussion.