Can you freeze orange zest and lemon zest?

Depending on what your making, yes. Since oranges and lemons are both citrus fruit they can be swapped aroung to change up tastes in food. But it still depends on whats being cooked because if you...

I would think so because the peels both taste the same bitterish taste

Zest is simply the peel of a citris fruit that has been finely grated. The peeling of these fruits has a more potent flavor than the fruit itself.

no because they are 2 different flavors and can have a different approach an flavorsbut it also depends an what your making

Lemon zest actually freezes very well, some they it even makes it more potent. There's a couple different routes you can take. First you can freeze the entire lemon and take it ouyt when you need it....