My partner and I have probably enjoyed close to 20 cruises, including NCL, Princess, Celebrity, Carnival, HAL and a few lines no longer around. Except for one cruise on a now-defunct cruiseline where ruby slippers appeared in the bar and hallways on the next-to-last night of the cruise, I don't recall ever feeling uncomfortable because of our gayness.
On our one and only HAL cruise, we were seated at a table with three generations of Mormon potato farmers from Idaho. Not only did we all enjoy each others company, but grandma wanted to sample all of our "adventurous" food choices, and mom passed all the drinks that were being sent to their very attractive daughter our way.
Overall, we prefer Celebrity for the quality of their ships, food and service. We'd rate Princess a close second, and we often sail NCL because of their prices and because we very much enjoy the freedom to eat when, where and with whom we want. However, we find that NCL is probably the least responsive to issues of any kind.
On our first Celebrity cruise on the Mercury, the Asst. Cruise Director hosted two FOD meetings and made us feel most welcome. Our last two Celebrity cruises featured non-hosted FOD meetings nearly every evening. We usually attend the first few, but have always found plenty of other GLBT folks around the ship or onshore to socialize with.
Regardless of the cruise line, ship or itinerary, we've always found that nearly all passengers quickly ID us as a gay couple and warmly welcome us. On our last Celebrity cruise around Cape Horn, a straight Southern Baptist couple from Waco, TX even invited us to join them at their dinner table after we played Trivia together.
So, in answer to your original question, our experience suggests that GLBT folks can probably choose almost any cruise based on the same criteria as non-gay passengers and feel most welcome.