I think the perfect response would have been “Don’t let the door hit you in the ass”, then start swinging it at them.
“Only when they are carrying doors”. Then you hand the door to them.
She wasn’t hitting on you unless she was an idiot. A proper lesbian would have asked if she could help you carry it!!! 
The part about “a rather cute, if large and soft, young lady, carrying a door through the rain” caused me to think of the Cowsills, which I would rather not have done.
If she was doing a survey, she’d probably skip people carrying heavy stuff–cute or otherwise–as they wouldn’t be likely to stop and elaborate.
If she was putting on the moves, I agree that she would have offered to help carry the door.
I think that leaves “being a twit” as the appropriate motivation.
Best response yet.
Ditto. This is why it’s always better to look pleasant but just keep walking.
Yeah, I’m with the “she was rude” people. The teens were probably giggling to themselves about whatever they decided was “wrong” with the people around them. They looked at the OP, decided that because of the non-traditional labor she was doing she must be gay. Finding this to be a mockable offense, one of them decides to confirm her belief by asking. When the OP wasn’t quick to respond, she tried “I’m doing a survey” and “I’m gay” merely as ways to convince the OP that it would be safe to respond truthfully - i.e. to confess her gayness.
All of this, IMHO, was to confirm some judgemental belief, whether it was “Gays are stupid” or “Lesbians are masculine” or “Woman doing hard labor is a closeted homosexual”.
Pretty much what I was thinking. It’s just nice to see so many others agree with me; makes a girl feel all warm 'n fuzzy inside, especially since I’d thought my thread here was on it’s way to being dead!
It would’ve been fun to swing a door at her, but with my luck, it’d hit her. She definitely wouldn’t be worth my job. I wouldn’t have been as polite as I was, but I have a hard time turning off Work Mode during my shift. She’s still a customer, after all 
In my book, not only were you sufficiently gracious, you also get points for thinking on your feet. If someone asked me “do you think about women sexually?” or any other equally inappropriate question, I might be so startled that I’d actually answer them before having the sense to counter with “why do you care?” Which is the right response, of course. Good for you.
Random thought: You could have said, “Does this look like a closet door to you? I can’t tell, but its fucking heavy!”
Sounds like her and her friends were trying to get off by picking at you. I remember groups of kids when I was younger always trying to bait me into stupid stuff like this. Usually with the sole intent of embarrasing me. Didn’t work, but that never made them not make the attempt. Reminds me of the jokes about calling a store and asking if Mike Hunt was there.
I don’t think there’s a better way to answer than how you did.
I appreciate your dedication to customer service but a rude customer is a rude customer. And this is outside the bounds of customer/serviceperson communication, unless you’re being paid to counsel troubled young people.