2. Everyone and their mother (in either party) can get away with portraying themselves as a "moderate", "centrist", "bipartisan," etc. these days even when they’re anything but. (Note that I’m not saying that Brown ever pretended to be moderate, I’m just pointing out that the term has lost all meaning.)
I think you're onto something, but I'd phrase it more as:
Moderate is a stance/public appearance, not an ideology. (Centrist, otoh, IS an ideology). A moderate has more to do with your public persona than your actual stance on issues. Rob Portman and Josh Hawley have basically identical voting records. Portman is a "moderate" because he speaks softly and doesn't insult people and acts with restraint, Hawley is a "hardliner" because he's a raving attack dog. The two's difference is almost entirely temperamental, not ideological.
("But Hawley's a populist!" How does that show up in his voting record vs Portman's, ever, in the nearly three years they've been in the Senate together? They're functionally the same as votes, it's all just stuff for the camera.)
Not to pick on Republicans here (well, yes to pick on Republicans...yes always to that) because the same is true with the Democrats. You're not going to find many votes over the last 5 years where Tim Kaine and Elizabeth Warren are voting on different sides, but Kaine's a "moderate" and Warren's a "progressive" for basically stylistic reasons.
