It's always difficult to answer such a question as there might have been a protest somewhere, so I will have to qualify my answer. I assume that by 'protests' you mean public mass protests. Despite having read lots of books on Anti-Imperialism and the Spanish-American War, I have not come across significant protests in the U.S. against the war itself. On the contrary, there were public mass meetings calling for war. Considering the situation in Cuba, the war against Spain could be fought 'for humanity' and was very popular.

There have of course been protests against the possible annexation of the territories acquired after the war from Spain and the Anti-Imperialist campaign. But these were usually not directed against the war itself and took place toward the end or after the war.

If you have any follow-up questions, I'm back in a few hours and happy to answer them.

Sources include:

Beisner, Twelve against empire: The anti-imperialists, 1898 - 1900

Linderman, The mirror of war: American society and the Spanish-American War

Tompkins, Anti-imperialism in the United States: The great debate, 1890 - 1920