I trim when I remove it from the washer - never have a problem with more fraying in the drier, and then the frayed strings don't cause problems with the fabric drying knotted up.
And I prewash everything - even scraps bought from others, and often have quite a tangled mess coming out of the wash.
Some fabric really frays, and some does not - I don't give it a thought.
I also put a large cotton towel (dry) in the dryer, and find that helps a lot with wrinkles.