This is dumb, but I really don't think a significant number of Latinos who would've otherwise voted Democratic are going to vote Republican because of this.
This specific point is not going to really change voters' minds, but it points to the reality that Democrats now are very out of touch with the concerns of the Latino community. Now does that mean Republicans are in touch with them? Probably not, but it will make it much harder for Democrats to retain their hold on the Latino vote long-term.
Yes, Democrats as a whole are not particularly in touch with Latino voters, but as you said, neither are Republicans. I don’t think Republicans are going to make further gains (outside of good years for their party) without some form of change to their party/candidates.