I'm not sure I'm entirely understanding you here. Do you mean that with NN the government could control free speech or that it would happen without NN? Government restrictions on what people can do online aren't inherent to the idea of NN. They'd be the opposite, really. Of course that's not to say that the FCC or other government agencies (in America and elsewhere) wouldn't try to propose both NN and some amount of government restriction concurrently, but AFAIK there isn't anything egregious in the rules the FCC has about free speech censorship. The main thing (aside from potentially gutting NN) that I think people worry about is spying on internet activity and government subpoenas for records from ISPs.
As for whether removing or weakening NN is likely, the big companies that provide internet would prefer to have no neutrality because then they could charge for different tiers of access.
Trump is a pro-business so even if NN is popular it's not necessarily popular to business types and Trump has already shown (like with DAPL) that he's capable of choosing a large business over the people.