i haven't mixed dancing & dating -- had many non-dancers who wanted to "take me out dancing" and i'd never ever go there. they wouldn't understand the culture of dancing with multiple partners all night... and i LIKE that culture!
now that i'm in a relationship with a dancer, we go to the same socials and mix it up the same as before... although we do dance together more often. he enjoys dancing with other women as much as i enjoy dancing with other men. i don't think it'd ever be a problem.
i generally only dance one (sequential) dance with someone, tho... on rare occasions, i may dance two sequential dances.
i've experienced sensitivity around asking a man to dance while out at a club, if his GF is nearby. has happened a couple times where i've asked the lady permission to allow me to steal her man away for a dance, and once the woman was very pissy about it. but she found me a few months later and apologized.
i don't worry about any of it, tho. i'm polite, and if someone has an issue, well... it's their issue to sort out. i don't believe i've ever given reasonable cause for anyone to take offense.
when i go latin dancing at clubs by myself, tho -- which is how i've almost always gone -- i tend to follow certain "rules" i've discovered which prevent one man from digging his talons in & trying to claim ownership for the evening. LOL