Water rower machine

Possibly holding the handle wrong. You don't need to grip it hard.

Just hook your fingers over the top so the handle sits behind just the outermost couple of segments of your fingers, with thumbs lightly underneath.

Let the slight tension of the cable hold it in place during the part of the stroke where you're moving back toward the tank (the "recovery" part of the stroke). Your leg push, body swing and arm pull put tension on it during the "drive" part of the stroke.

The tension hold the handles in place against your hooked fingers quite steadily. There should be no need for the handle to move around within your hands/fingers. There should be minimal rubbing or friction to create blisters.

You can wear gloves if you like, or fingerless ones like lifting or bike gloves, depending on where the blisters are. Gloves may or may not help.

On-water (boat) rowers normally do not wear gloves, because we need to feel the water contact through the oar handle. We sometimes do get blisters, but that's because we need the oar handles moving against our hands to do some aspects of bladework. Rowing machines should not very much have that problem.

Good luck!

I wear fingerless leather palmed nylon backed climbing gloves both lifting and rowing.