I guess it's somewhat situational, but more times than not there will be different behavior amongst heterosexual males just because of that. So yeah, the guy might be doing other things because the other party is a woman. What if it's just to look good in front of women, despite not being interested in them? I've seen that happen. Some guys just feel good on the attention that may be gained. They aren't necessarily sexist.
You've basically just said there "Someone isn't a sexist because they are doing sexist things", I hope you see the contradiction there
If you are doing a thing for one gender that you are doing because they are that gender then it is, by definition, a sexist act because you are applying discrimination with regards to your actions based on gender. As to if it is a problem or not depends on the act, the intent and the outcome but it is still by the definition a sexist act.
I guess the point is that, in many small ways, we all do sexist things even if it is as simple as sexual preference in partners - the problems arise when those things are done which cause others problems be they physical or mental issues. Even something as small as holding open a door for a women, if you only do it for women, has the underlying issue that you seem to think they can't do it for themselves which might, if someone constantly witnesses this, cause issues. (I'd also argue that not holding open a door for everyone makes you a bit of a dick ;))