Well, firstly I don't think it's possible to weed out religion from popular culture (which accounts for the religious undertones you mentioned). That would just be ignoring history and precedent, ie: people in the west expect their holidays during what are religious dates because that's when those holidays always were held, and it just carries on (and similarly, a lot of those holidays have their origins in even older pagan rituals that were borrowed for the same reason of "it's what's familiar"). I don't believe that's necessary in any case.
Secondly, there is a definitional problem as well. There are plenty of "secular states", ie. states that do not meddle in the affairs of religions and don't profess any specialized support for any. Not just western states either, the former Soviet bloc countries and their affiliates were all officially secular states (more so even than western ones). Many of them made a point of really pushing secularism as well