Unfortunately, the Mexican border has never closed. It is open to Mexico bound tourists and inbound to the U.S. for Americans and American nationals (permanent residents non-citizen).
Mexico is a hot spot with over 106,000 recorded deaths and according to a group of six ex-Mexican national secretaries of health, as high as 285,000 deaths.
We have friends in Hidalgo and McAllen and it's bad right now. We have lost one friend or colleague every two weeks for the last four months. One is on a ventilator now in critical condition, her brother came to Mexico to visit and was positive but didn't know it. Mexico is only doing a temperature test if that. Big mistake.
The state of Arizona makes it very clear that there are no travel restrictions or testing requirements.