Not too long ago, I attended a "dati" [religious] wedding. I came late and when I arrived I wasn't sure if I was at a religious, spiritual union celebrating the start of a holy union that will last for all the generations - or a disco. The answer was .... both. A Jewish boy was marrying a Jewish girl כדת משה וישראל. I am sure she went to mikva before the wedding. They will keep Shabbos and kosher and give their kids a Jewish education. The food served was all kosher. No lobster served. Good for the Jews. Good for the lobsters. But all of the kids were out there on the dance floor boogeying away. Males, females, married, single. I would have joined but there were some obstructions. One was that my wife wasn't there and I had nobody with whom to dance. Even if she was there, she is not exactly the type.... There were other "issues" that I had. So I stayed long enough to wish the chattan a warm mazel tov and I was outta there. The dancing I am sure went on through the night. Young people would say "it rocked".
I'm not critical of these people. I love them. That is why I almost danced with them...:-) But this is a phenomenon. It is quite common for weddings both in Israel and outside, to start with some old fashioned separate sex dancing and then the "nigginum" change, the mechitza is removed [if there was one in the first place] and the mixed dancing begins. The men are wearing kippas. The ladies all received a religious education and wouldn't dream of eating on Yom Kippur [actually - many of us dream of eating on Yom Kippur as we sit in shul due to our hunger but that is besides the point] or driving on Shabbos. So what are you? A halachically observant believing Jew or a chiloni who has no problem publicly mixed dancing?
Both.
R' Dovid'l of Tolna said that the world is split up between half believers and half non-believers. He clarified that what he means is that in EVERY PERSON there is this dichotomy [he didn't use the word "dichotomy" but that is what he meant]. His task was אריינשינין אמונה - to shine emunah in the hearts of Jews.
I believe that this holds true today and explains mixed dancing at religious weddings and many other things. The same G-d who said not to marry a non-Jew that kippah wearing and Shabbos observing people would never do, is the same G-d who said not to have mixed dancing or watch immodest movies etc. etc. But somehow people can live this dual lifestyle of consistently following G-d in certain matters, not following him in others, fasting and apologizing on Yom Kippur and then continuing on the same path after Yom Kippur.
A great sevice would be done if we were able to strengthen religious people to become Baalei Teshuva.
We can start with ourselves...:-).