I like accents
My theory on the subject is this: If you're moving to a place where the national language is Gibberish, you should learn at least basic Gibberish. It doesn't have to be profound; you don't need to be able to read Shakesphere in Gibberish. But you should be capable of going to the store and buying your groceries in Gibberish. (Note: This does not mean you shouldn't be able to speak your native Gobbleygook at home or with friends. That is wonderful and perfectly acceptable! You should not talk about Gibberish speakers in Gobbleygook where the Gibberish speakers can hear you. That is very rude.)
If you are in a specialized career you should learn the appropriate jargon in Gibberish. If you are working with the public at all, your Gibberish should be good enough to communicate with your client base. You should be allowed to have slip ups, without fear of being ridiculed. Native Gibberish speakers make mistakes, too. And your Gibberish can be accented, lightly or heavily, so long as it is decipherable.
It's okay to go through a learning phase. Just make sure you are trying
to be helpful and communicative, rather than sullen that the Gibberish speaker doesn't automatically know Gobbleygook.
My only other suggestion for "assimilation" (which generally only needs to be minimal anyway) is that if you move somewhere where the dress is more conservative, you are more conservative in public; if you move somewhere less conservative, you should still dress to your level of comfort.