Non-Muslims are religiously not permitted to enter the holy mosque of Mecca or Madina (Prophet’s mosque). The Saudi government also prohibits people from entering the city. Moreover, one cannot enter Mecca without ihram, so therein lies the restriction anyways. Sayyid Sistani says it is not permissible to enter the city of Mecca without ihram (except for a few cases, which would not apply anyway), thus it would be impermissible for them given they don’t wear ihram