That's speaking as someone who would like to see clearer legal protections for content-neutral hosting platforms.
Thats a slightly different, but related [0] effect. The NRAs own PR approach has made special deals with the NRA a PR liability for many businesses. Public relations aren't something companies burn money on for entertainment value, they do it because corporate image impacts the bottom line, because it has a direct effect on things like consumer choices and ability to attract and retain talent.
[0] related in that lawsuits are also used to address political issues (and targeting tangentially-involved businesses formgun violence is a well-known example of that), so that the public mood on gun policy that shapes the reaction to NRA PR efforts also is a factor in the legal risk that firms face with Section 230 being weakened.
This is the chilling effect from the attack on Section 230 safe harbor protection (an attack which was largely “justified” by conduct which was already found to be outside of the pre-existing safe harbor, and so which needed no modification to deal with.)
Companies that are being responsible to their shareholders are going to change behavior to minimize exposure to content which is likely to draw civil litigation when their protection from that risk is weakened.