Of course "preventing online censorship" in the name means this order creates censorship. If websites today all became liable for user-provided content there's no way in hell that in 2020 you're going to get nearly the same level of protection back in a new replacement law.
Look at the DMCA which in 2001/2002 everyone and their brother hated online because any company could take down a file from your website with just a letter. Nowadays DMCA counterclaims and the "burden" of sending notices to websites would never be included in any copyright law. The MPAA/RIAA, wouldn't let that kind of law get passed these days.
edit: there's a lot to parse in this order. It looks like it's trying to limit any possible political censorship. But in general I'm against regulating websites regardless of the intentions.