We live in a cisheteronormative society in which, yes, absolutely, the way someone's gender is perceived impacts how people interact with them.
I (trans man) generally don't treat my friends too differently based on gender, but there are definitely some differences between my relationships with women and my relationships with men. When I hang out with other guys, there's a lot more "dude", "man", "bud" in conversations (obviously). When I hang out with women, conversations about feelings and personal issues are more common, and so are hugs/embraces. This is pretty much entirely "code switching" for me, and not a case of me imposing that this is how relationships with a certain gender should work.
I should point out, though, that this is not 100% based on gender and gender only. It's largely about the personality, and we live in a world in which there is a strong correlation between gender identity and personality traits (see: gender roles and stereotypes), and so gender can often (but not always) act as a shorthand for that. As a counterexample, someone I know is an effeminate (cis) guy, and I'd say that our conversations and interactions feel more like the ones I'm used to with women.
Your question's made me curious; you appear to be binary trans (please correct me if I am mistaken!) Prior to making this post and having this discussion, what had the concept of passing meant to you? Was it purely about automatically being referred to with the right pronouns and terms (son/brother/etc) without having to say anything? Or was there anything more to it?