Persuading the population at large, fine. Persuading (or attempting to persuade) businesses to do what you as government aren't allowed to to do is Bad. There is a fine line between persuasion and coercion when the infinite power of government is doing the persuading. Dangerous to freedom.

Is it, though?

This puts me in mind of the efforts by past Republican governments (federal and state) to work with faith-based organizations (ie. mostly churches) to try to cut down on teenage pregnancy. Those efforts didn't involve the feds "coercing" those institutions into doing something the government couldn't do directly. The government, of course, is forbidden from making a religious argument in favor of abstinence - but because that's something that the churches already wanted to do, the government was using funds and resources to try to help them do it better.

That's almost certainly what the government claims is happening here. They portray these efforts as "helping" Facebook and Twitter (and others) implement policies that those organizations already had. For example, they want to prevent their sites being used for the exchange of forbidden child sexual material - so the law enforcement agencies that investigate the trafficking of such material will alert them to groups of individuals that are using the site to facilitate such exchanges so that Facebook and Twitter can block them. That helps the government achieve its goals, of course; but ostensibly, Facebook and Twitter independently want to throw those folks off their site as well.