Stupid poll is stupid, for bajillions of reasons already explained. Sex object or women are inferior? Hmm. I vote potato.
Women can do anything they... qualify to do. And there are some women who can qualify to do almost anything in the military. Probably not a majority, as has been mentioned, but if they can do it there's no reason they shouldn't be allowed to.
But this is a really weird one...
Women need a lot less food than men. A LOT. In biological terms (and this is typical of most primates), males need slightly more than their environment typically provides, and women need dramatically less. So even if women actually did require more calories during menstruation, it would still be a lot less than a male requires.
There are also products to deal with menstruation that would cause virtually no strain on the military. No waste, an entire day of management, dirty cheap. Not a problem.
In reality, most women don't spend all day being miserable from their period. Mostly hardly notice except when they have to actually change out whatever they're using.
Menstruation does not impair a woman. If it does, then she has a medical problem, and her finesses in light of that should be assessed like any other medical problem.