How is it bad faith, and how is that in any way connected to the letter? I'm really trying to understand what you're trying to get at, and I'm struggling. The closest to anything coherent I've arrived at is something along the lines of "some people, a subset of which are progressives, agree with what Biden did, therefore it's bad faith for other people to disagree with what Biden did [potentially especially so if the people disagreeing are progressives, somehow?]", but I doubt that's it.
As for "In the sense that people don't say "Hmm I disagree with these criteria", they say "Biden should have vetted!". Feels weak.", that is saying they disagree with the criteria used, because they're saying that individual vetting should have been one. Implicitly, by the kids for cash judge being mentioned, they're saying that "not engaging in child slavery" should be a criteria, for instance.