I don't care:

[daleduke17]

if you're black, white, tan, yellow or any other color.
if you're gay, straight, bi, or whatever.
if you worship Jesus, Mary, God, Joe Pesci, the fates, nature, whatever.
if you think your kid is "special" (read: helicopter/show/pageant parent)
if you're male or female.
if you eat meat or vegetables.
if you are from Mexico, Japan, Texas, Ohio or Nunavut.
what you call yourselves this week. Handicapped/handi-capable/physically challenged, black/negro/African-American, gay/queer/homosexual. I can't keep up.

Just, I don't care. Please don't care about what I am.

[draggar]

Good call.

[elsporko]

I care if people eat meat or vegetables because it affects what restaurants I can take them to.

[HYHYBT]

Mostly, no, I don't care. But:
Appearance: If I have to give a description of you, I care very much what you look like. Also, see orientation and sex.

Orientation: If I'm thinking of asking you on a date, it matters very much!

Religion: Because I find comparing religious beliefs interesting, I do care what religion you are; beyond that, when I was doing schedules it was important. It also matters very much if you're trying to use it against me, especially if we're supposed to be in the same one.

Sex/gender: If I'm going to refer to you in the third person, it helps to know whether to use male or female pronouns. Also, as with orientation, for certain purposes it matters very much!

Meat/veg: If I'm cooking or shopping for you, I care what you eat.

As with religion, I *do* care where you're from; as with religion, it can be interesting to compare and sometimes it helps to understand people better. For a very literal example, I once had a new boss who sounded incredibly rude, until I found out she was from New York City and just had a very strong accent; my Georgia ears needed that context to adjust.

[Bloodsoul]

I do care if you have little chunks of carrot stuck in your teeth.

I'd have that taken care of; I hear it can lead to insanity.

[Wingates_Hellsing]

I don't care about any of those things in that I don't think any of them make you a good or bad person (add political views in as well) but they're good to know for a great many practical reasons, as illustrated above.