1. Stop thinking you're intruding, duh.
2. Where I live, there's no such thing as a male privilege, except maybe a traditional preference for males in high, leading jobs like directors and politicians... even though it's changing as the old men are retiring.
Actually, I've only ever hit a female privilege that I lacked. It's not exactly a positive thing, but nowadays, females are stereotypically regarded as superwomen who can take care of children alone, work and imply themselves in their community, all responsibly, whilst males are supposedly sexual, aggressive and misadapted people who can only barely manage a job, failing to take care of housework efficiently. It's like men are women's children. It's not to such an extent, and it's not in everyone, but it's sort of the idea that's going around. Like it's revenge for past sexism.
Females are more regarded than males in many sectors, be it social relations or even work. For example, a theatre once turned me back saying that they didn't hire guys.
Also, females who work in traditionally male environments (computers, mechanical and construction workers, truck driving) are usually encouraged, whilst males in the opposite position (secretaries, nurses, children guardians) are generally disregarded ("it's gay!") or distrusted ("you'll rape my children!")
All that to say that no, I don't feel I'm losing any male privilege.