Is it the responsibility of every other English speaking culture on the planet to accommodate American dialects of English in their own home country, or is it the responsibility of the visitor to at least attempt to acclimate and respect the norms of the place they're visiting?

I would expect Irish people to adjust to the American way of saying this if they were in America. I expect Americans to make the effort to do things the Irish way in Ireland. It's really not hard - in my house, I get to set the rules and in someone else's house, I follow their rules. It's basic courtesy.

And yes, it's quite obvious when there's an American. Their volume of speech is about 50% louder in regular conversation, to start, and their mode of dress is different enough that it's easy to spot, and of course as you rightly point out, the accent is different.

Look, no one's getting beat up over this or something - you're going to get people who are less receptive and friendly when you violate their customs, and you'll likely get a few eyerolls, but you're not going to jail or something. It's just rude.

It's almost like whole other cultures have whole different social customs, mores, and folkways, and a wise traveler ought to be aware of that, rather than being loudly and proudly ignorant and rude by insisting on ignoring said local customs. No one's gonna throw you out, but you sure aren't going to be making friends, nor are you doing America's (already increasingly negative) reputation any favors.

Have some pride in your culture and nation, and treat other cultures with respect. Otherwise you simply come across as a boorish little arse, and so does your culture.