I have spent many years studying martial arts. I am the only woman in my club at my level of seniority.
The men that I train with regard it as somewhat of a compliment to tell me I am 'one of the lads' or 'one of the guys'. I see why they think that, and that it is well intentioned, so I usually just crack something along the lines 'cept the ovaries, eh?!' which isn't really a joke, I'm just saying it like it's a joke, and they laugh along, and we all elbow each other and say things like, 'heh, heh, heh!' These slightly ridiculous exchanges come about when someone has made some dubious joke about 'five finger technique' or whatever, which is, just to be clear, an innuendo and not something to do with the actual martial art. Such discussions usually happen in social situations.
The real reason that I make the response I do is partially because I like to remind them that that female bodied people can 'do' martial arts, have that same identity as them, that same experience, which quite often people think of as a masculine right of passage. More importantly, though, it's worth subtley reminding them that they can have relationships with female bodied people based on who they are and what they are like, rather than on the fact they are female bodied and should therefore be considered for these kinds of relationships but not those ones. I'm trying to say, 'no, this is not 'guyness' we are sharing, because I'm not a guy, what we are having is a relationship - we're relating to each other and it's not because 'we're all guys here!'
What effect this has on anyone is probably limited. But I do prefer to insist that I am female bodied rather than accept the 'one of the guys' mantle. I'd rather not be explained away as an anomaly or as an exception, which is what 'one of the guys' actually tries to assert. But I don't think that offering me the option to be 'one of the guys' is actually that respectful, I think it is a way of coming to terms with the fact that I am not in fact a male, but here anyway. So are 'the guys' wrong about what they assume women are in relation to 'the guys'? Or is she just some misfit that leaves the overall order of things undisturbed? I support the former position, so always assert my femaleness in some way when this comes up.