I got turned off from Levertov's poetry by a few things. A friend of mine gave a scathing critique of one her books, Candles in Babylon, and I kind of agreed with it. The professor was a friend of hers and didn't like my friend's critique.
She turned increasingly devotional and political in the later work: I preferred her earlier work by far. Whereas Creeley welcomed the language poets and was generous to younger voices generally, Levertov tried to nix Perloff's appointment at Stanford, distributing a letter to all the faculty of the English department, in part because she championed the language group. Perloff got the job, but the letter seemed nasty to me. We all (the grad students) saw it as well.
That being said, I did sincerely like her earlier poems of the 50s and 60s, and I'm going to go back and read some of those earlier books. She was an enormously talented writer in the WCW vein, and I think she has fallen out of fashion somewhat, where Ronald Johnson and others once on the fringes of the Black Mountain group are in ascendence. Perhaps the religiosity got in people's way.