I am sure, given the events last week, that security will be exceptionally tight and heavy. If protestors arrive for the inauguration (and I'm sure there will be some), they will be kept a long, long ways back, and given that the media covering the event will not want to have it upstaged in any way by a loud and negative protest, they will probably not be covered in any significant way, save a passing note in the news that they were there, if even that.
I don't think it will require the Republicans to do or say anything. No one will want a repeat of what they saw last week, and security, to some degree, seems to have a bit of 'mud on its face' for failure to either anticipate the eventual surge, or to contain it, or both. Some leaders of law enforcement, including the sergeant-at-arms of the House and others have already resigned. You can be sure there will be a visible military presence to back up law enforcement. If protestors are there, and they are shouting, they will hardly be heard anywhere near the White House. And given the control of this event I highly doubt that any violence will be evident near the event.