In general, Christian philosophers and apologists are hostile to the multiverse, because that appeal is often used to nullify the fine-tuning argument or the strong anthropic principle. Two notable exceptions are Don Page and Jeff Zweerink.
I don't object to the idea of a multiverse. By that I mean I don't think there's anything antecedently unfitting about God creating an ensemble in which alternate timelines play out.
The problem is when a multiverse is derived from a particular interpretation of quantum mechanics. The theological problem with the many-worlds interpretation of quantum mechanics is that rather than having a selection of parallel worlds based on divine wisdom and benevolence, you have an indiscriminate totality based on physical determinism. The result is that many parallel worlds will suffer from pervasive gratuitous evil. If every physical possibility happens, then there will be actual universes in which everybody is damned. Fallen worlds without redemption. Fallen worlds with no compensatory goods. I think that's incompatible with divine wisdom and benevolence.