I've been on two cruises. I'm transgendered and in a lesbian relationship--we have a 9 year old daughter. I've never had any issues on either cruise. I've no idea who can tell if I'm trans or not though. I transitioned almost 15 years ago, IDs match, and I've had enough surgeries for a small town, including Dr. Doug's 10 hour facial rearrangement. I'm rarely if ever misgendered and long ago stopped worrying about it. So maybe not a perfect example as maybe nobody even knew.
Our first cruise, we shared a table and the other family was very quiet, but I suspect they were very quiet in general. And so are we. Or maybe it was the lesbian parents thing. One never knows, but if they were that bent, I think they would have requested a new table, not come back nightly for more abuse. And we did the usual chit-chat about things. It certainly wasn't something that affected our cruise, more that after we thought "oh I wonder..." We requested a private table for our second cruise simply because we are anti-social types in general.
My general feeling is that DCL is incredibly good to their guests and that includes LGBT people of all kinds.
I can on speak as a gay male couple, but our experiences on three cruises have all been wonderful. No issues with our tablemates. No issues with any of the servers, cast or crew. We were even selected to participate in "Match Your Mate" on one cruise based on the cheers of the crowd (and we won).
The only ... slightly "negative" incident I can recall is one night we were walking back to our room (simply walking side by side in the narrow-ish corridor) and a presumably heterosexual couple walking behind us who had (again presumably) been drinking said (more loudly than I think they intended) something along the lines of having seen so many of "those types" (i.e. gay couples) on the cruise.
This is a relief to hear. I've sailed twice before with friends, but next year will be the first with my wife. We have matching shirts and I got a small rainbow Mickey rainbow magnet to go with the other magnets on our stateroom door!