I don't think of this as "subversive" unless they are doing something like rigging elections by assisting illegal immigrants in voting. But you are correct that pro-immigration advocates often attempt to demonize the other side. Sometimes they sincerely believe that immigration reform advocates are motivated by racism (some of the pro-immigration folks are lefties, after all). But some of them are just cynically trying to smear their opponent so they don't have to debate the issues.
There was a good example in the news Thursday. Arizona Congressman J.D. Hayworth was speaking in favor of a CFR amendment that would bar political contributions from legal immigrants. He was attacked as being "xenophobic" and being against Hispanics, even though his remarks had to do with the Chinese contributions to Clinton-Gore.
There's no remedy for this except to keep pointing out where such statements are unfair, and at times, absurd and hateful. And I'm an optimist in that I think in the long run such rhetoric by pro-immigration speakers backfires on them. The American public eventually sees through stuff like this when it is pointed out.