The answer is the sun.
"I turn polar bears white"
Polar bears have clear hair shafts, so when light from the sun's rays reflect off them, they appear white.
"and I will make you cry."
When you look at the sun, your eyes water, making it seem like you're crying.
"I make guys have to pee"
The sun coming up in the morning wakes you up if you've been sleeping, and most of you know that soon after you wake up, you have to pee.
"and girls comb their hair."
The sun brings light, which brings visibility to our world. Girls, once it is light, worry about being seen. They comb their hair to look better in the light from the sun.
"I make celebrities look stupid"
Everyone who's read People Magazine knows that celebrities can look stupid. The sun is the provider of light for the stupid pictures that have been taken.
"and normal people look like celebrities."
Just like the sun sees/makes celebrities look stupid, it can make normal people look like celebrities. Both are possible with the right lighting.
"I turn pancakes brown"
The brown on pancakes is just reflected light, which comes from the sun.
"and make your champane bubble."
The sun's light catches the champagne bubbles, causing them to sparkle. Without light, they wouldn't be visible.
"If you squeeze me, I'll pop."
This line probably originated from the previous line's image of champagne bubbles "popping." But if we were to squeeze the sun, which is a ball of gas, we can imagine that it would pop.
"If you look at me, you'll pop."
Again, the word "pop." The repetition is obvious. "Pop" in this situation means to destroy. Did your mother ever tell you not to look at the sun? Mine did. She told me that it would destroy my vision, making me go blind.