A great many Christian denominations will use the word “catholic” in the generic sense of “universal” in their beliefs about themselves. An anglo-catholic would believe themselves to be part of the universal Church of Christ, but just part of the anglo branch. In their thinking, being in Communion with the Pope is not necessary for membership in the universal Church, believing in Christ and that He is the head of the universal Church is sufficient.
Keep in mind that many Orthodox believe themselves to be Orthodox Catholic, because, although they are Orthodox, they are part of the universal Church of Christ.
If you review the Nicene Creed in almost every denomination that uses it, you will find the word “catholic” spelled without capitalization, thus meaning “universal,” not “(Roman) Catholic.” Even the Catholic Church does not currently capitalize the word “catholic” in the Creed.