Out of the politically active population, there would be some who wanted to become a US state, some who want independence, and the rest who wmay have a preference but be willing to accept either provided they received other concessions.
There will definitely be hardliners unwilling to accept Cuba as part of the United States, and some kind of insurrection is inevitable. Provided the United States has the political will to accept casualties until the insurrection is crushed, and provided the United States and Cuban collaborators are politically savvy enough to structure a deal that causes most of the independent supporters to accept statehood, then it's possible for Cuba to become a state (or states).
I think it's a very strong challenge to accomplish all of that, but it is theoretically possible.
In the long term, improved public health will allow lots of white Americans to immigrate to Cuba, changing the racial mix. Yellow fever is certainly bad, but it was during this time that Dr. Walter Reed and others discovered its transmission vector and was able to fight it. Since the US was able to build the Panama Canal soon after this time, it won't be long before white Americans could begin moving to Havana and elsewhere and have a good survival rate.