While there are certainly many unions that do not discriminate when it comes to who they try to organize, this is not true of all unions.
One of the arguments sometimes used by organized labor is that the hiring of illegal immigrants drives down everyone’s wages. Because the immigrants are afraid of getting caught and have nowhere else to go, they are willing to accept much lower pay than those living here without fear. It’s hard to enforce minimum wage or work safety standards when the employees are too afraid to come forward – so the employers that hire these immigrants have an unfair advantage in the market.
My brother says, "It's not about giving a man a fish, and certainly not about teaching a man to fish... it's about letting a man fish!"
I certainly agree with this. Instead of fighting illegal immigration, organized labor should encourage the immigrants (and themselves) to simply take democratic control over their places of work, because even if they managed to send all the immigrants back to their countries of origin, their jobs will be shipped overseas anyway, in search of people willing to accept lower pay and with less rights to organize.