Praise be to Allaah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him, who answered as follows:
This matter needs further examination, because the place is not appropriate, except in the unlikely event that it might be said that the Muslims are so powerful that they can proclaim their religion in the places of worship of the Christians. If this is the case, then it is good. But I am worried that it may be the opposite, i.e., that the Muslims are compelled to speak of their religion in the church. Hence I think that he should not do that, in order to avoid falling into this category (of being weak). And Allaah knows best.