Why is it that illegals can buy real estate in this country & in Mexico a non Mexican can only lease?

Not only can a non Mexican only lease. Mexican nationals are also given preference over non Mexicans in hiring. Its their law. They also have much higher restrictions regarding immigration.

I don't have a good answer, just a true one. The U.S. financial institutions will support the purchase of U.S. properties in the form of loans, this creates revenue. The banks see this as reason enough to lobby government officials to write laws that permit the sales.
Mexico's government forsaw America buying their country one piece at a time a wrote laws to prevent a financial take over of their government.