Correct. And, as an aside, this is the way the right ought to be framing this subject if it wants to cut into the DNC monopoly on Latino votes.
I happen to own a business that occasionally employs immigrant workers. Of course we do what is required by law to make these men verify their legal status to work in this country. I can assure you and everyone else reading this that these men are more strongly opposed to illegal immigration than anyone you meet. They also side with the right on social issues, like abortion and gay marriage.
However, in an election, those who can vote will probably vote for the Democrat candidate. Why is that? Because most of them do not pay a lot of attention to politics in this country, or even watch English news programs. What they hear about the candidates is that all Republicans hate brown people, because that is the headline when the leading GOP candidate says that rapists are included in the illegals coming into this country and the liberal media repackages this into "Trump says all Mexicans are rapists."
You're right on this issue and we DO need to get the word out to our fellow citizens who happen to be Hispanic. One problem our side has is elites like Jeb who want to pander to what they imagine is the Hispanic position and tell a disturbing and condescending story. Her's another shocker - a lot of Americans who just happen to be Muslim DO NOT want Muslims from Syria flooding the country.