Mexicans rarely or never come under these headings. Most valid caes involve Chinese (forced abortions), Albanians (political persecution), Iraqi Christians, Cubans, some Sudanese and Mauritanians (oppression by Muslim Arabs v. black Christians or pagans). Most invalid ones involve phony claims of any of the above.
But, it's not "PC" anything -- it's a legal category, which people are entitled to apply for, per laws pased by Congress.
Has been used in the past by Jews from Europe, Hungarians after 1956 revolution, Vietnamese and Laotians after the Dems sold them out, etc.
1. my post was sarcasm
2. Cases are in Texas... Why would asylum seekers be entering the U.S. illegally through Mexico? (That's what the article said.)