People who think hugs are weird, are weird. I have no invasion of space issues here, but I can understand a bit of weirdness.
I usually associate prolonged (more than second) physical contact with something romantic/intimate, so I only truly liked hugs from the ex gf. She's the only one that I'd really hug...I'd squeeze the stuffing out of her several times a day. Everyone else gets a perfunctory hug.
Hugs from Mom are ok, from Dad less so...but not awkward or uncomfortable. Other hugs are just business-like, and rare.
I'm not especially warm or demonstrative, but I do believe that physical contact (whether it's a hug or something else) is important, saying "I love you" is also important...just showing your love in general. I think it can make a difference in oyur overall health and well-being.
It's hard, we take it for granted, etc...but it's the better way to be.