There are no Christian churches (or any non-Muslim houses of worship) in Mecca.
Mecca is Islam's holiest city. Entry is strictly prohibited to non-Muslims by Saudi law. The entire city is a haram (sanctuary). Only Muslims may enter, reside, or worship there.
Non-Muslim expatriates in Saudi Arabia worship in private compounds or designated areas in other cities (e.g., Jeddah, Riyadh)—but never in Mecca or Medina.