I am literally a political science major they absolutely care, care about their image that is. Even if a conservative gets a ton of emails and calls from their constituents supporting the cause there's no way in Hell they're going to back something specifically mentioning sex work and porn. Meanwhile a progressive may be all for that and claim it empowers females, this has been said about OnlyFans workers by far left politicians.
Wording is very, very important as is what is included. It's why you see a lot of smaller items such as relief aid or education support tacked onto military or similar bills because then major supporters of the primary subject of the bill can then cry out loud that those who vote against it don't support the smaller tacked on subjects.
Politics is very much Hollywood. What you say and how you look is often far more important than what you actually do.