I wouldn't say it's generally considered false, considering that the company founded on this assumption - Vanguard - is now the largest fund in the U.S. and second largest asset manager in the world.
Markets are interesting, though, in that the more people believe they are efficient, the more inefficiencies creep in, and the more people believe they are inefficient, the more they become efficient. When everyone assumes everyone else has found all the opportunities, nobody bothers to look, and so there are lots of undiscovered opportunities to cash in on. When everyone assumes they can get rich finding opportunities, they bid up prices to very close to their "true" value, and the profit opportunities disappear. It's a self-correcting system.
The question of how widely believed the EMH is itself suffers from selection bias. People who believe markets are efficient don't enter the financial industry, they give their money to Vanguard to manage. That means that everyone in the financial industry, by definition, believes that they can make better-than-average returns, otherwise they wouldn't be in the industry. And then by returns, most of them are wrong, but that also doesn't matter because the few who are right are the ones who survive to play the next round.