My guess is the sun!
I turn polar bears white - Polar bears have clear hair thus the sun light makes it look white
and I will make you cry.
ever tried to look at the sun?
I make guys have to pee - Dunno here but every morning when the sun rises I gotta take a piss.
and girls comb their hair. - too much sun = dried out hair = frizzly hair need to be combed
I make celebrities look stupid - Sun burned Carrot top FTL
and normal people look like celebrities. - a nice tan anyone?
I turn pancakes brown - put batter on a sidewalk on a hot day in Phoenix and see what happens
and make your champagne bubble. - dunno, maybe it affects the carbonation
If you squeeze me, I'll pop. - ever hear that the sun will eventually implode, I guess you could say it is being squeezed
If you look at me, you'll pop. - If forced to stare at the sun long enough I'm sure at least a blood vessel will pop.
Can you guess the riddle?