When LadyTango and I were house-hunting (December 2012-January 2013), we took our shoes off for about half the houses we saw. No one asked us to do so, but we made our decision based on the condition of the house (i.e. if we would be comfortable living there without redoing the flooring, we took our shoes off. If the flooring was really dirty or unfinished, we left them on.)
Given the way the real estate agent was acting, I would probably not want to work with them again.