For example, I have heard rumors that Mike Pence has association with churches and organizations that subscribe to Dominionism Theology. Is a question to in/validate these rumors on topic here? If so, the follow-up question of which flavor of Dominionism (if the initial claim is substantiated) he is associated with on-topic?
Are questions about the stances (political/religious) of specific politicians or political appointees on-topic here?
Yes, questions about the political positions of notable politicians are on-topic. But please try to focus on their actual position according to their own statements and actions. Do not fall for the guilt by association fallacy.
Religious believes not so much, unless they demonstrably affect their politics.
By the way: There is also Skeptics Stackexchange, which specializes on confirming or debunking claims. But keep in mind that questions over there need to follow formal criteria. For example, questions must refer to a specific claim made by a notable source.