No, there is not any evidence that justify the prohibition of Non-Muslims to enter these cities.
The problem arises from the misunderstanding of verse 9:28 in which Allah the Almighty commands:
“Believers! Those mushriks* are nothing but dirt. So, after the expiry of this year, let them not even go near the Sacred Mosque. Should you fear of poverty, Allah will enrich you out of His bounty if He orders so. Surely Allah knows and commands rightly.”
Those mushriks are the ones mentioned in the first six verses of the same chapter. Let us fill you in from the beginning.
When mushriks were trying to uproot the messenger of Allah from Mecca, they were warned by this verse:
“They were bent upon uprooting you from this land and driving you away from it. But were they to succeed, they would not be able to remain after you more than a little while. This has been our way with the messengers whom We sent before you. You will find no change in our way.” (17:76-77)
After the conquest of Mecca, mushriks had not been touched for 15 months until they started to violate the treaty they made with Muslims. Then with the sending down of these verses below, they were announced by Allah to leave Mecca for a punishment of their violation or be killed.
“This is a declaration of last admonition from Allah and His Messenger to the mushriks with whom you had made a treaty. Travel freely throughout the land for four months but know that you cannot weaken Allah and know that Allah will disgrace the concealers. An announcement from Allah and His Messenger to the people on the day of that great pilgrimage: Allah is disassociated from the mushriks and so is His Messenger. So if you repent, that is best for you. But if you turn away, then know that you cannot weaken Allah. Inform those who conceal the truth of a painful punishment. Except for those with whom you made a treaty among the mushriks and then they have not been deficient towards you in anything nor supported anyone against you. Fulfill for them their treaty until their term. Indeed, Allah loves the ones who guard themselves. When those forbidden months have passed, kill those mushriks wherever you find them. Capture them, besiege them, sit and wait for them at every place of ambush. But should they repent, establish prayers, and give the tax, then let them on their way. Surely Allah forgives and shows mercy. If any of those mushriks seeks asylum, grant him asylum that he may hear the words of Allah. Then escort him to safety. This is because that they are ignorant people.” (9:1-6)
Another verse related to those people is this:
“Kill them wherever you encounter them and drive them out from where they drove you out since persecution is worse than killing. Do not fight against them near the Sacred Mosque unless they attack you there. Kill them if they attack you there. This is the punishment of those concealers.” (2:191)
Unfortunately, people that cannot combine and evaluate verses all together with their background interpret them to their liking and believe that all non-Muslims can be killed or driven out from their homes. According to Quran, no Non-Muslim can be treated unjustly let alone killing them, unless they kill Muslims because of their religion or expel them from their homes.
Allah the Almighty commands:
“Allah does not forbid you from being kind and equitable to those who do not fight you because of religion and do not expel you from your homes. Indeed, Allah likes those who are equitable. Allah only forbids you from making friends of those who fight you because of religion or expel you from your homes or aid in your expulsion. The ones that make friends of them are the wrongdoers.” (60:8-9)
Preventing non-Muslims from entering Mecca or Medina has nothing to do with the religion of Allah. It is indeed an inequity for them.
* Mushrik means someone who joins others with Allah. This occurs either by attributing supernatural features to something/someone by seeking a supernatural kind of aid from it/him, or adopting a system of values from something/someone rather than Allah and giving it/him the first priority in his/her decisions.