It doesn't bother me at all. Both my girlfriend and I are post menopause, we were young once!
There's two ways of going down on a woman on her period- Licking her clit, and sorta trying to keep your face from making too much contact, or just diving in face first, because you know it just blood, and it washes off.
Sometimes it's an accident. You come up for air, and your girlfriend is shocked, or starts laughing, cause your face is covered.
Other times it's just plain on purpose. You're both horny, she removes whatever protection she's using, and away you go!!
Personally, I have a thing about all things menstrual. I'm probably the only woman on earth with a menstrual fetish, but only for other peoples menses. I have a fascination with used products, and bloody vaginas. I can stare at one for hours. I like fingering them (or more), so it would be hypocritical not to enjoy oral on them. I like to push my tongue in as far as it will go, and spread their lips wide. I've no doubt swallowed menstrual blood, but that was more just a by-product of what I was doing.