Except if the rules are always different for me, it sort of means I'll never belong here. When people open up about what they think of Americans, I sometimes wish I hadn't brought it up. Apparently we're big and noisy and aggressive. Also, we eat funny and talk through our noses.
Everywhere has stereotypes about people from other places. Overweight and loud would both be common beliefs to have about Americans, I've never heard eating funny and talking through noses before (although the French have a stereotype that Americans speak without opening their mouths.)
As for belonging - that's surely for you to decide?
My grandad, an Englishman, moved to rural Wales in the 1950s, to run a hotel in a seaside village, employing a number of people. He learned to speak Welsh, became a local councillor, was a preacher in the local chapel and was involved in preservation of the local steam railway. When he left after 15 years, there was a collection to buy him a present and wish him well; the speech began "although Mr xxx is a stranger here." I think people are much more willing to accept others now.
I've lived around Cambridge for 20+ years but will always consider another part of England as "home" even though I have no intention of ever living there. The vast majority of adults who live in this area are not from here originally and of course there's a significant number for whom English is not their first language.
I meant to pass on some comments from an American colleague who spent a couple of months here over the summer. One was "why do British people end texts with xx or xxx?", another was "why is TJ Maxx called TK Maxx in Britain?" She was also surprised to find that fortnight is a word in regular use and that we don't use creamer in hot drinks.