Moment Magazine has an article about synagogues and churches that share spaces (only a small excerpt is available online). Interestingly, the author asked R. Hershel Schachter his view on the matter, although from his answer it seems that he might have been asked a slightly different question. He stated his opposition, based on halakhah, to a Jew entering a church. R. Yitz Greenberg was also asked, and he gave some non-answer about how halakhic changes take time.
The following letter from R. Joseph B. Soloveitchik is relevant. He was asked about the architecture of a proposed interfaith chapel and was specifically told that the existence of such a chapel is not under question but only details about it. R. Soloveitchik answered those questions but also felt obligated to state his view of interfaith chapels. Community, Covenant and Commitment (pp. 8-9):
I strongly object to the use of an interfaith chapel. The Halakhah is unequivocally opposed to it and this prohibition is even more strict than that concerning human images... The idea of a common house of prayer is absolutely irreconcilable with the Judaic philosophy of worship. This attitude stems neither from intolerance or narrow-mindedness, nor from a feeling of superiority or dogmatic charism, but from a depp philosophical insight into the essence of worship... The holiness of the synagogue, like the sanctity of the home, finds expression in our respect for tis privacy and exclusiveness. To be dedicated to a plurality of cultic modes is a pure paradox.