If a Puerto Rican became citizen of México & than renounced their American citizenship can they come back to United States visit?

If you renounce citizenship of a country, you can realistically expect never to be allowed back in

They would need a tourist visa, as does any Mexican. They likely would not qualify for a tourist visa, due to ties to the US.

Both Mexico and the USA allow dual/multiple nationality so there is no reason for a US citizen who obtains Mexican citizenship to renounce their US citizenship.

Another answer is correct and most people who renounce their US citizenship are not allowed to ever return to the USA. There are exceptions, but generally only when the individual ha no choice. An example would be a person who is a government official in anther country who is prohibited by law in that country from holding another nationality while employed as a government official.

Many Americans who have become citizens elsewhere & renounced their US citizenship apply for & obtain 10-year multiple-entry tourist visa (B1/B2). Of course, they can only enter US for vacations, tourism, visits.

Depends on how he did it. If he did a proper expatriation and filed the 8854 form at an American consulate, he would have received a multiple indefinite tourist visa stamp in his Mexican passport.

As long as the person did not later overstay or attempt to work on that visa, it should be fine. I know a number of people who have done exactly that. Who wants to pay US taxes if they do not have to?

Yes, but as the bearer of a Mexican passport they’d require a tourist visa to visit or a work visa to work.

Not without a visa

And most times when someone renounces their US citizenship they are never allowed back into the country

Sure... they need a Visa just like any other Mexican