That's not how the first amendment works, as it does put limitations on the kinds of speech that governments are allowed to favor (or disfavor). Just saying it only affects employment or contracts does not act like a "get out of jail free" card for governments.

Of course, there is a ton of gray area here that the courts will have to rule on, but the whole point the ACLU is making is that they believe these anti-boycott laws are in violation of the first amendment.