In general I believe that immigrants to this country are more liberal leaning then conservative, so they would naturally favor the democratic party over the republican party, the democratic party is more social values and taking care of everyone and the republican party stresses personal responsibility, so it's not very surprising that immigrants would generally dislike republicans.
I don't think the only reason immigrants don't like republicans is more then a stance on limited government and personal responsibilities. It could be alot more then that it could be the way they act, what they support and what they do to help out the country and help people
I won't agree with this point on principle, since the comments seem to be at least borderline racist and is a huge over simplification. Still, for immigrants, the appeal of having a large government is largely because of what they can get for free. This is rational - the very poor, newly arrived aren't really focusing on ideology when they have to struggle for every meal.
Immigrants hate the Republican Party because the GOP hates immigrants. It's that simple. The Republican Party is the party of white America. Sure, they go to great lengths to try and appear otherwise, but that's who they are at heart. That's also we immigration reform always fails. The GOP blocks it.
When shoring up the numbers, it becomes clear that a staggering number of immigrants to the United States every year arrive by illicit or otherwise underhanded means, and that such immigrants do not have a legal right to live or work in this country. Given this, it seems clear that most immigrants would be against Republicans due to their harsh stance on illegal immigration and strict immigration laws.