This open-access article by the historian Peter Nosco mentions both the Kakure Kirishitan (hidden Christian) communities and the Kakure Nenbutsu (hidden Jodo Shinshu) communities in Kyushu, and offers some limited comparison of their experiences during the Edo and Meiji periods, but makes no mention of interaction between them.
https://www.jstor.org/stable/30234176
I suspect that, considering how insulated such communities were, they didn't engage, or at least we have no records of such engagement. It also is worth considering that shared opposition to an oppressive government would not necessarily allow them to overcome their different religious world views.