There have been polls, with a dramatic range of support. Wikipedia leads me to the most MWI-friendly poll. I think the low-water mark is about 10% of some other group of quantum theorists. I suspect that the variation is due to wording issues and local social pressure (by "local" I mean the conference), but the page suggests different communities:

The findings of this poll are in accord with other polls, that many- worlds is most popular amongst scientists who may rather loosely be described as string theorists or quantum gravitists/cosmologists. It is less popular amongst the wider scientific community who mostly remain in ignorance of it.

Antia Lamas saw MWI win a poll for least favorite interpretation. On that page, Michael Nielsen mentions a poll where MWI came 3rd, after Copenhagen and decoherence...but if decoherence is an interpretation, it sure sounds like MWI to me.