Time is short. A few thoughts:
1) The subject is not anywhere as clear cut as Kasha makes it out to be. As Reb Moshe dismisses right away in his teshuva, Al tarbeh is only a midas chassidus. That means advice that Chazal give. Often Chazal use extremely strong language to discourage certain things, when they are actually even permitted or far less severe. Chazal even warned about idle chatter with the same gender in Kesuvos (Al yashmea devarim betailim lozno, mipnei she hen nichvos techila l’avarim). Chazal wanted people to focus on accomplishing in Torah and Chochma and Chesed and not to get sidetracked with things that can potentially consume all one’s time. As always, seichel rules the day. If a wife needs time with her husband or if a poor almana needs to be comforted, one should give them al the time they need. This is chesed, no different than any other.
2) Note that Lo Tinaf is a bein adam lachaveiro. This is why one who would not save a woman for fear of touching her is a chasid shoteh. He thinks he is doing a mitzvah, when in fact the whole purpose is not to take somebody away from her husband. Therefore, when touching somebody’s wife will save her for her husband and loved ones, there is no issur.
3) Note that Beruria who used very harsh language to Rebbe Yossi that he wasn’t frum enough, ended up being seduced by a Talmid elsewhere in shas. (Rashi in A”Z?)
4) The Rabbi who told Oomis that women don’t need to wear nail polish ever is quite disconcerting. Do men ever need to wear ties? Do people ever need to buy art for their walls? Do women ever need dresses, sackcloth works just as well. Do women ever need jewelry? Do people ever need orthodonture, if they are not in any pain and can eat? What on earth did he mean. Note that the Rambam at end of Chap 11 of Issurei Biah states that women should always use all their makeup even during niddah so they remain attractive to their husbands. it is a shame when women misunderstand tznius and think they are doing a mitzvah by dressing as a shmatta.
5) If an opposite gender relationship can potentially lead to marriage, how in the world can it be assur? How is it different than dating. There is no shiur on how many dates one is allowed to go on.
6) As far as shaking hands with a non-Jewish woman for business, consider the following. What is the worst that can happen? Suppose the man actually did a complete maaseh with her. What did he violate? Answer, a drabbanan (Rambam based on gemara in A”Z). So how severe could shaking hands be? the analogy to Kashrus seems to be difficult, because A) that is deoraisa, B) that is bein adam lamakom, whereas this is bein adam lachaveiro. In addition, I heard in the name of one of the acharonim that not only is it muttar, but if one doesn’t shake the hand of a woman who extends it, it is a huge chillul hashem and makes Jews seem like barbarians with no manners.