The idea of religion and (biological) "race" being separate categories didn't really get started in Britain until the mid-19th century. Before then, the concept of race had a lot more to do with religion, language, and culture than it did physical appearance.

That said, whether you could improve your caste rank by assimilating into the majority culture (converting from Catholicism to Protestantism) tended to boil down to your resulting marriage prospects. If you were lucky, the caste system in your time and place practiced "hyperdescent" (children of a mixed-caste marriage go up in rank), instead of "hypodescent" (down in rank).

As for the Anglican Church, before Victorian times they actually condemned "polygenism"--what we'd now call scientific racism--for contradicting the Biblical single origin of Adam and Eve.

(Source: Normans and Saxons, Richie Devon Watson, Jr.)

Back when? Scientific racism emerged and became a powerful force from mid-1800s to WW2. It's when the type of modern racism you're probably thinking about emerged. However, you do have people like Edmund Spencer in the early modern period writing things like

the Chiefest [nation that settled in Ireland] I Suppose to be Scithians ... which firste inhabitinge and afterwarde stretchinge themselves forthe into the lande as theire numbers increased named it all of themselues Scuttenlande which more brieflye is Called Scuttlande or Scotlande.

Scythians were seen as the epitome of savagery and barbarism (thanks to how the ancient Greeks portrayed them). To the point it was believed the Scythians feasted on their own children. Basically, saying that the Irish descended from the Scythians was saying their form of civilization was always barbarous. Not quite modern racism, but not just religion.