FWIW, some conservatives argue that what private companies do is their business. These blacklists are where that thought eventually leads, but it’s supported by some nevertheless.
What this group is attempting to make these companies do is wrong. But if a company decides to go along just how would you have them compelled to do otherwise?
Blacklists can cut both ways.
That sounds like something that libertarians who call themselves conservatives argue. I’d refer them to Article 3 Section 3 of the Constitution that they claim to revere; and also to Goal #37 of the 45 communist goals for the USA, which states: “Infiltrate and gain control of big business.”