Rashi disagrees and holds that if the sanctity of the Beis Hamikdosh ceased by its destruction, it would be permitted to offer sacrifices on a private altar nowadays.
The commentators ask on Rabbeinu Chaim: If the sanctity ceased after the destruction, why would it be forbidden to offer sacrifices on a private altar? After the destruction of Shiloh, bamos became permitted, so why not after the destruction of the Beis Hamikdosh?
Minchas Chinuch (254:7) writes that although Yerushalayim has lost its sanctity in regards to offering sacrifices and eating Kodoshim, the city remains the “chosen place” and the third Beis Hamikdosh will be built there. This is why private altars are still forbidden. This is the distinction between Shiloh and Yerushalayim. Shiloh was not the chosen city and when the Tabernacle was destroyed, there was no vestige of sanctity left in the city and bamos became permitted. Minchas Chinuch states that this is the explanation as to why we are still subject to a prohibition of fearing the Mikdash nowadays, since it is still the chosen place although it has not retained its sanctity.