So my main question is that if you are a parent (or not) would you allow your kid to have a member of the opposite six over?
Not having any children, I honestly have no idea how I'd approach anything 'parental'.
What do you mean by having your girlfriend over? If you're just hanging out with her in a family room watching movies or whatever, then I can't see a problem, and I think your parents are being pretty odd about it. But if by 'over' you mean in your bedroom with the door locked and loud music playing, then I can see their point somewhat.
EDIT:
Well according to the OPs profile, he is 23.....if this is the case......something is a bit wrong there IMO.
You're right - the OP is the same age as me. I'm lucky that my parents have been fairly liberal since I was 18, but I guess as long as you live under their roof, you're subject to their rules. While I don't agree with their principals personally, you're pretty much stuck with their rules until you get a place of your own.