You get the same sorts of problems with mixed faith marriages as you do in mixed race marriages. It may not always be apparent to the people actually getting married. But it will likely have consequences for your kids.
We reconciled it by getting married twice. Once christian, once shinto (both equally meaningless , but for the benifit of our families).
It's much more difficult to reconcile religions as they are just inherently unreasonable.
Grandparents will probably be your biggest cause of conflict. Not so easy to ignore as the populace in general.