
Nyerkh |

Wildblooded is technically an archetype, or at least follows the same rules.
Both it and the Mongrel alter the Bloodline feature - the Powers as well - which means they can't be stacked.
That's it.
Could you houserule it without breaking everything ?
Mostly yes, with some exceptions (Sylvan being the big one). Doesn't seem like that will be good enough for your GM though.
Wildblooded makes a lot of things blurry, if not weird. It's important in these cases to keep in mind that it is, in fact, considered an archetype (or close enough).
Eldritch Heritage comes to mind (though there's a feat for that specifically).