Separation of Church and Prof?

For the second straight year, I have had a student approach me on this day in the Jewish calendar to wish me a Happy New Year.  One could suggest that these students are being perceptive since I was born into a Jewish family.  Or one could suggest that they have a poor sense of boundaries since I only look Jewish/sound Jewish (I complain a lot).  But I am not at all a religious person.  Indeed, I am pretty anti-religious when it comes down to it.  So, it feels mighty awkward to me. 

I guess I would never have imagined approaching a prof with an assumption about them and then acting on it.  I know there is no ill intention--obviously, the opposite.  But I still think that my religion or lack thereof is a private thing (only fit for blogging).  I do mention other private things in class, like my family to illustrate various concepts (like my strategic dogs and what they imply for strategic thinking), but I never identify myself by religion.  So, is it appropriate for students to assume that I am of one particular sect/brand/whatever and then appeal to the imagined community that the student thinks we share?  Again, I think not. 

This never happened before the last couple of years.  Are folks being more presumptuous or am I just becoming too approachable and informal in class?  Your guess is as good or better than mine.