They didn't protest, really. They spoke out when it came time to sign the "Articles of Continental Association" that circulated throughout the country in 1775 and 1776. Loyalists refused to sign this document, while their Patriot neighbors did.

Once the war broke out, Loyalists either joined up with a Loyalist regiment, left their homes for Loyalist-controlled areas (like Long Island), or stayed put and kept their mouth shut. Some of those who stayed put did work for the Loyalists in secret, and there was a commission set up by Congress to discover and prosecute any Loyalist activity.

Likewise, the Brits also tried to root out Patriot activity in American territory that they controlled.

But once the war broke out, if you were in Patriot territory and tried to make any public display of support for the Loyalist cause, you were very likely to get yourself thrown in jail or worse.

That said, there were people who spoke out and stood against Congress, but not necessarily pro-Loyalist. After the Declaration of Independence was signed, George Washington lost a series of battles and there was a lot of public blowback. That diminished shortly after, with his famous Crossing of the Delaware.