Do American Hispanics' self described racial identification tend to line up with their political views?

In the 2020 US Census, the percentage of Hispanics identifying as white alone dropped by over half. I'm curious about the differences between those that checked white as their race, "some other race" (usually a write in for "Hispanic" or related terms), or neither of those (most often "two or more races" or "Native American").

In the United States as well as parts of Latin America from what I've read, identifying as non-white is often on average associated with more liberal views because of history with European colonialism and other things. Has there been any research within the Hispanic category in the US on political leanings along these lines?

Note: I'm not specifically asking "what percentage of Hispanic voters who selected some other race on the 2020 Census voted for Biden in 2020's presidential election" or anything else like that though such a statistic could be helpful.