Were cubans subject to racism?

No not in the terms of your question. Cubans were (are) Hispanics. Hispanic people were never enslaved or lynched or any part of 'Jim Crow'. Spain and it's colonies in the Americas had a long history alongside the US. They did however (except for wealthy Cubans) face common ethnic prejudice from the white 'anglo-saxon protestants', but then they put everyone down.

if you call brown on brown in Cuba racism yes -- ,, there were no Cubans for the most part in the USA during Jim crow years after the USA civil war 1870s+,,, the JFK era 1960s was when the Cubans began coming to the USA to escape Tyranny of Castro --- History is to be learned from not to find things to be mad about 

the lesson of Cuba is Socialism and Communism do not work 

Cubans were far less likely to feel the fullest brunt of persecution. The hardcore racists back then were almost exclusively targeting blacks as the most inferior.

Cuban migration has not been happening for a long time.  Its only been happening since the Cuban revolution of 1959.  Before that Cuba was on par with the US.  Since then, it has been frozen in time for the most part.  People who can leave, did leave under Fidel Castro.  There only place to go was the US.  The US policy at the time was stated that if you made it to land, you could stay, however if you were caught at sea, then you would be returned to Cuba.    Its that type of policy and isolation from the US market that has kept CUBA where it is after the fall of the Soviet Union.  Up until the fall of the soviet union, the soviets were injecting loads of cash into Cuba in order to keep it a float.  After the fall of the soviet union, the money dried up and they have had to survive on their own.  

So no, Cubans were not subject to Racism in the same way African-Black people were.  No Cubans were not slaves in the US.  (Please read about triangle trade that promoted slavery).  Cubans are Spanish decent, not African decent, so they are viewed as Latinos..