Non-muslims are not allowed in the sanctuary of the Sacred Mosque in Mecca based on the following verse:
Quran 9:28 O you who have believed, indeed the polytheists are unclean, so let them not approach al-Masjid al-Haram after this, their
[final] year. And if you fear privation, Allah will enrich you from
His bounty if He wills. Indeed, Allah is Knowing and Wise.
The scholars of Shariah are all agreed upon this, though the Hanafis interpret that they may be allowed entry in certain conditions, though all agree that they can not be allowed open entry, or to perform the pilgrimage according to their own rites and beliefs (IslamQA, Hidayah) .
Non-muslims are allowed entry into Medinah, and they may visit other mosques based on the actions of the Prophet and the Caliphs as detailed in the above sources.
Related answer: https://islam.stackexchange.com/a/30307/20218