Many Latinos/as don't like the Left for 3 reasons:
1. The term Latinx is the 6-letter word, the X word and even insulting to feminists, non-binary and LGBTQ, Jewish and BIPOC, and allies in the social justice movement, it's not a real word in standard Spanish whether in Spain and Latin America, and the small subset who used Latinx (4chan admittedly tricked them in the late 2010s) now want to adopt "Latine" as a new non-malecentric, gender neutral and less machismo style way of a collective term of 25 nationalities of Spanish and Portuguese origin in the Americas and western hemisphere plus former Spanish or Mexican ruled border states TX, NM, AZ and CA.
2. actually, lumping Hispanic/Latino persons in the people of color category isn't fully received, and they blamed that issue on liberal racists LBJ, Nixon and Goldwater, their affirmative action policy is very racial and based on biological race theory, even though the category isn't racial at all, it's ethn linguistic, and liberals argue conservative SCOTUS judges are practicing color blindness, there should be repatriations for pre-21st century immigration Hispanics (also a not so liked term, ask Cheech Marin who popularized the term Chicano for himself) we know as a country there are conservative Latins and many like the anti-Castro Cuban community concentrated in south FL are the most registered Republican ethnic groups, are quite Americanized, its some of their (grand) parents obsessed with remaining Cuban without actually setting foot in the home island 100 miles away still never learning any English.
and 3. 2nd generation born to Central and South American immigrants aren't the same like US-born Mexicans like Tejanos, Hispanos and Chicanos...or Puerto Ricans in the 50s. I know the earlier generation Mexican Americans and stateside Puerto Ricans are said to emulate urban Black culture, but earlier immigrants and the first Spanish Americans in the southwest US were labeled white before the 1930s when they were lumped as a Mexican race, Indians (or the "Asiatic-Mongoloid-Oriental"race) or coloreds (the lumping with Blacks came in), even comparing Spaniards who are Caucasians from Europe with Jews, Arabs, Roma people and Asian Indians as if they are "brown" or "mulato" type of Europeans, noticed the 1930s Mexican immigrants were into intermarrying white ethnic catholics (Italians are compatible until the war Italians became white like French Canadians, Poles, Germans and Irish), Chinese or Japanese (and many Filipinos), Armenians, Asian Indians, Pacific Islanders and of course, California tribes, but until WW2, they couldn't marry Blacks other than they may cohabit with them (which was a taboo anyway).
In Coachella Valley CA where I live: its perfectly OK for a person with a mustache wear a dress (esp indigenous Mexicans, the majority of immigrants, came with legal permission with, and had amnesty for overstaying their work visas have that concept of gender identity diversity), just don't assume all will refer to themselves as Latinx (or Hispanic or even Mexican), and be in mind there are Black, mixed with Anglo (northern Mexico had many 1800s-era Germans), Chinese / Japanese/ Korean (Mexicali-calexico), and even (mostly Christian) Arab Mexicans and Latinos.