That is not what the quote means:
By "protest," Gertrude doesn't mean "object" or "deny"these meanings postdate Hamlet. The principal meaning of "protest" in Shakespeare's day was "vow" or "declare solemnly," a meaning preserved in our use of "protestation." When we [sic] smugly declare that "the lady doth protest too much," we almost always mean that the lady objects so much as to lose credibility. Gertrude says that Player Queen affirms so much as to lose credibility. Her vows are too elaborate, too artful, too insistent.
To me, the quote from Mr. Trump about his faith seemed too over the top for credibility. Some other Freepers suggested that I watch the whole interview, which I will try to do at a later time.
And why do you think she loses that credibility? It’s because she’s being hypocritical and doesn’t really have an issue - ergo, she has the problem she protests against.