Could believing that "all men are abusers" contribute to staying with the one specific abuser?

Sorta, yes, no. Cart before the horse. I think some women who stay with abusers may rationalize it by believing that all men are abusers. Mostly rationality is used for "understanding" what is happening, not generally to prompt fundamental changes. When I was drinking I had a very warped idea of how much other people drank, I thought I was drinking a little more than them. When I stopped drinking, and especially when I stopped feeling driven to drink, I realized that a tremendous fraction of my world was barely drinking at all, and that even among drinkers, most of them were sober enough to read the bill at the end of the night (which I generally wasn't on Fridays).

The evidence about other people's drinking was always there, I discounted gigantically its difference from what I was doing. In most of modern life, the evidence for other men treating other women differently is there, the question is why would one woman in an almost identical information rich environment as another women never give a guy who once raises his voice at her a second chance, while another stays through multiple mate-induced hospital visits?