There’s never been any manufacturer’s statement warning about adverse effects of being vaccinated while infected. There’s no danger in being vaccinated while infected other than that the previous infection won’t be prevented.
The 4 strains cause nearly all the problems with genital HPV in the US. Two of the strains (16,18) cause 70-80% of cervical cancer and precancerous changes. There is some evidence of cross-protection from strains other than the ones in the vaccine.
I think the issue is more on cost/benefit than on safety here. While the risk from being vaccinated against a strain that one has already been infected with is negligible, the vaccine is expensive.
I work with a gynecologist currently; she tells me the vaccine is $125 per dose, with 3 doses recommended. She doesn’t see the point in vaccinating people who won’t benefit.