Can Muslims go to churches and temples, for the sake of learning about other religions? Also can non-Muslims visit the Holy Ka‘bah and other mosques for such purposes?

Muslims can certainly go to the places of worship of other religions to learn about them. When they do visit such places, they should be very respectful and observe the proper etiquette. Of course, if necessary, prior permission should be sought from the concerned authorities.

The answer to the second part of your question is that only people who have adopted polytheism as their religion (as some Hindu sects) are not allowed to visit the Holy Ka‘bah. It was about the pagan Arabs who had adopted polytheism as their religion that the Qur’ān declared:

Believers, verily these idolaters are unclean [of faith]. So let them not after this year of theirs approach the Sacred Mosque. (9:28)

It is evident from this verse that the real reason of this prohibition is polytheism which has been called impure and unclean. Consequently, this prohibition stands analogously extended to people who have adopted polytheism as their religion. It cannot be extended to the adherents of such monotheistic religions as Judaism and Christianity. Though the followers of Christianity are involved in idolatrous practices yet they never condone to idolatry as the real religion. It must be appreciated that there is a world of difference between getting involved in idolatrous practices while considering them to be non-idolatrous and becoming followers of idolatry itself.

Moreover, as is evident from the verse quoted above, this prohibition for the polytheists is just for the Holy Ka‘bah which is the ultimate centre of monotheism. They can visit other mosques if they like.