liberal base is in theory pro-union and pro-worker, but will immediately guillotine any internal party member who suggests economic discrimination in favor of native-born industries and workers.
Well, yes, because discrimination on the basis of where someone was born is illegal. The American liberal base is, and has always been, fine with economic discrimination in favor of those in America (without regard to where they were born or their residency status).
There is a stereotype that conservatives are "less fine" with outsourcing than liberals. I'm not saying it's strictly true, but it's a very strongly embedded stereotype if it's not true.
Also, you're resigning the biggest part of the conversation (immigration and residency policy and enforcement, especially with regards to employment) to an implication in a parenthetical?