Is it important? Well.....somewhat. But there are a lot of things that are way more important, like the general levels of good relations you maintain with other people, for example.

Besides, if we reincarnate many times, and I think we do, then cultural heritage is just a brief and passing role that only encompasses one life. It can enrich that life, for sure, but you generally find yourself dealing with a whole new situation when the curtain rises again on a new life, so why get overly attached to any one culture?

This makes no sense at all to someone who thinks he's only here once, of course, and I wouldn't expect it to.