I don't hate RR, but not a big fan of it. Besides that the chorus sounds like just bunch of words to me, when she sings the words "renegade runaway", it sounds like the lyrics are strained in the way they are sung. Not that Carrie is straining to sing them, she has no problem with it at all. I just don't like the way it sounds. Not sure anyone will get what I mean by "strained".
See, I see the production as totally different than what she has done before. I agree lyrically it falls in line, but they could have sold at least me on it being a new sound.
Before the release, Carrie spoke a couple of times about the album having more of a "twang rock" feel (or "rock twang", I forget exactly how she put it). There's quite a bit of twang in RR - you can hear it plainly in the introduction, and, for example, around 1.30. The choruses have a particularly up-tempo rock feel, and this is also varied with a significant amount of twang. What I think Carrie is trying to do with her vocal is give it more of a raw edge, with a "breathy", rushed effect, to avoid giving it too much of a "belted" vocal sound, which would tend to suggest a more Pop-influenced feel, which would not be consistent with the twang in the music. So, in my opinion, rather than jarring with the music, I think the "strained" effect is actually complementing the music.
Whether people like it, or would prefer a more conventional vocal, is obviously a matter of personal taste - but I agree with Adam that this is one of Carrie's experiments on the album with a different sound. I do like it - and I also think that Carrie will benefit from showing variations in her singing style - this being one of them (though not the only one).
I do agree that the lyrics could be considered a bit formulaic - the song does have something of the feel of a "made for the hit market" number. But I think Carrie and Jay are trying to do something different with the overall sound. The combination of the two aspects make me feel this is pretty likely to be released as a single at some point (and I've felt that since first hearing the album)