Orthodox Jewish men (or at least some of them) believe that they cannot sit next to a woman not their wife. As such, according to an article in a recent New York Times (you may read it here: http://www.nytimes.com/2015/04/10/us/aboard-flights-conflicts-over-seat-assignments-and-religion.html??WT.mc_id=2015-APRIL-AOL-EMAILED_AUD_DEV-0401-0430&WT.mc_ev=click&ad-keywords=AUDDEVAPRIL&icid=maing-grid7%7Cmaing15%7Cdl8%7Csec1_lnk2%26pLid%3D641839&_r=0 ) there have been flight delays caused when an Orthodox male refused to sit immediately next to a woman. How might we address such concerns?
The best way may be to accept that there is a difference between solely religious beliefs and real secular intrusion upon religious rights, and that reason can determine where one trumps the other. After all, and we will argue this as axiomatic, no true religion can violate reason. Similarly, no illogical societal prohibition on a given religious practice should be used to impede that practice. If a seemingly religious practice is itself unreasonable, then the general society has grounds to ignore it. If it is reasonable, then society must allow and even arguably make accommodations for it.
In this case, the idea that merely touching a woman not your wife violates the sanctity of marriage is unreasonable. If it weren't, then a male priest baptizing a female infant would be wrong; even such mundane things as a hug or handshake between a man and a woman would be immoral. In short, the simple and incidental touching of a woman whom a man is not married to is not, by any reasonable standard immoral. As such, society may rightly refuse to recognize that any religious right exists on that ground.
This is not to single out Orthodox Jewish men. We're, ahem, reasonably sure that similar conflicts can be found within Catholic, Protestant, Islamic or almost any other creed. Neither are we trying to suggest that every conflict between religion and society can be so readily addressed or dismissed. We will even admit that the case here is so clear (accepting the Times reporting as accurate, and there is no compelling reason not to) that Orthodox Jews on the whole accept what society says on the matter.
But that's part of out point. We're admittedly using a question with an obvious answer just to show how reason should be applied. The line will be more difficult to draw as the issues grow more complex and heated. But at the end of the day what we need is for both society and religion to seek, accept, and live by and within a rational framework. If we can do that, then we all ought to get along just fine.