Dear Rabbi, I would like to know why the minhag of ’mitzvah tantz’ is not a tznius issue. I am not questioning the minhag. It was created well before my time and by people much, much greater than any of us. Yet the thought of a chosson dancing hand-in-hand with his kallah ’bifnei kol am v’eidah’ seems to me to be somewhat lacking in tznius. The same way one wouldn’t show public affection to his wife in the street, why isn’t a dance in front of extended family and close friends considered ’chiba b’farhesia’?
The minhag, as described in Hanesuin Kehilchatam (ch. 13 n. 89), is for this dance to take place at the very end of the seudat mitzva after the sheva brachot that follow Birkat Hamazon when almost all of the guests (and all of the unmarried men) have already left for home. Still, if this is not your minhag, you should not adopt it - for the reason you mention and others (the dance may embarass someone who cannot participate in it because she is not tehora).