Do trolling motors get in the way of fly fishing even if it's mounted out of the way? I mean you always see fly fishing guides using a push pole in saltwater.

Pretty sure that they're using a push pole because it's quieter than running a motor. That being said, there is a sort of Murphy's Law about fly line tangling on anything and everything. I have fished out of plenty of boats with trolling motors with no extraordinarily bad results.
Cleats, outboards, lights, my feet, anchors, it's all snaggy. But don't let it stop you because it ain't that big a deal IMO.

Yes, trolling motors, trolling motor foot pedals, fish finders, dogs, and everything else on the deck will get in the way of the fly line. You eventually learn to work with it, although the dog doesn't always co-operate. Push poles don't work very well when the water is deeper than several feet, so they're not always an option.

Yeah, I knew they used push poles to be stealthy but I didn't think it was a big difference between a trolling motor, is there? I asked because using a trolling motor is way easier than using a pole but was worried about catching the motor. What if i used a stripping basket?

We've gone to stripping baskets / barrels .. whatever ... on deck, and that helps a lot. A lot of guides are realizing they can do better for their clients with a trolling motor nowadays, and have detachable mounts on their trolling motors up front. They also use a remote control, so they can be trolling and poling their clients for a more relaxing and productive outing. I used to think I didn't want a trolling motor, but not anymore.
If nothing else, to clear line grabbers, take a beach towel, wet it and lay it over whatever is hanging onto your line (except your dog of course).

That's a good idea about the wet towel and the dog ! And it makes sense for guides to use the remote controlled motors instead poling, much more relaxing, more time to spot fish, and when used on a low setting it's as quiet as poling. Thanks!

I think the poles become more effective when the TM starts churning mud or trying to hold in one spot up shallow. Seems it's better for sight fishing.

If the TM isn't touching anything it should be fine...annoying at times, of course! I tend to stand back a bit further from TM when fly fishing. It helps. Also keeping everything off the deck helps too.

Push Poles definitely have their place but you have to compromise boat size for poling success.