This is total BS. Besides, I have seen polls where majority of latinos opposes illegal immigration so the idea that latinos are pro-illegal is likely not true.
If large part of majority would think that murdering annoying neigbor is ok, this does not mean that GOP should embrace it. Instead, it means GOP should educate and argue why it is bad.
Likewise for illegal immigration. GOP should explain clearly why it is bad and explain the true cost (financial cost and daily murders and loss of life due to DWIs)