How do you finish the edge of ceramic tile next to edge of metal frame sliding door? Do you butt the edge of tile to edge strip or leave 1/4 inch gap for grout?

William rossbach

Don't leave a 1/4" thats too big of a gap. If you can leave an 1/16 -1/8" gap that would be better. Then seal this joint with a caulking close to the grout or tile color.
If you grout the joint, the grout may crack and come loose due to the expansion of the alum. Door track.