I think it's definitely possible to learn from the two traditions and practice elements simultaneously... but I think it's not possible to be both on account of the different end goals. Practice must be done with the end in mind. Also, unless you have a solid founding in one before investigating the other, you're bound to get incredibly confused!
If you mean support in the sense of donations, offering etc. then of course that would be OK. I'm Theravadin but I drop a coin in the donation box at the local Mahayana centre when I go there at lunchtimes to meditate.