Generally, yes. If you are referring to the Catholic Church, then “Catholic” and “Church” should be capitalized since they refer to a proper noun. If you are referring to someone who practices Catholicism, then you should capitalize Catholic as well.
When would you lowercase Catholic?
When it first entered the English language in the 16th century, catholic meant “common” or “general” so the religion was naturally the “common” religion. When the Western Church split from the rest of the church after the Reformation, it began referring to itself as the Catholic Church, but the word catholic still meant “general” or “common” when used by itself.
What about Catholicism?
Since Catholicism is a noun referring to the Catholic religion, it is capitalized as well.
To learn more about proper title capitalization rules, give our free title capitalization tool a try.