Can two antennas in proximity interfere with each other if they're not amplified?
For the wavelengths you're trying to receive, keep everything else more than 1 wavelength away. So for VHF FM radio keep other antennas or metal that would act like an antenna 10 feet away if you're trying to pick up far away stations. Same with UHF TV, 2-3 feet away is good for a far away station. 

In reality though, most signals/stations are so powerful that a little signal attenuation won't make a difference. With digital TV there is error correction as well, so you either get it or you don't unlike analog TV where you deal with all kinds of noise. 

If you need to share a mast, then just do it. Ideally you'd have a 300 foot tower too, but most signals are so strong you don't have to. Worst case just get a higher dBi one to offset any losses.