I have a small travel tripod that can fit in my backpack when I wear that. I have also brought a full size (well maybe 3/4 size) that will fit in the lockers at EPCOT and DHS, but not at MK.
It can be a pain to carry it around, but the lockers are a big help. If your tripod doesn't fit in the locker you can leave it at the cashiers desk where you pay for the locker.
I've taken night shots with a tripod at the 4 big parks and a few hotels and really enjoy it. Haven't taken any at Downtown Disney (not that you can't, I just haven't).
The only people that will give you a hard time are other guests who will think that your a photo pass photographer and they'll hand you their photo pass and want you to take their picture.