catholic = rechtgläubig is correct
It is, however, one of the MANY meanings of catholic (A II 6b, see below, from Oxford English Dictionary)
Most people do not know these meanings of catholic. Therefore many protestants say for example "I believe in the holy CHRISTIAN church", instead of "I believe in the holy catholic church". The Anglican church, however, still maintains the "catholic" in the apostolic creed, so you will hear "I believe in the holy catholic church" in an Anglican church and the do of course not mean Roman Catholic.
A. adj. I. In non-ecclesiastical use.
1. gen. Universal.
2. In specific uses: a. Universally prevalent: said e.g. of substances, actions, laws, principles, customs, conditions, etc. Obs.
b. Universally applicable or efficient; spec. of medicines, remedies. Obs.
c. More loosely: Common, prevalent. Obs.
d. Entire, without exception. Obs.
3. In current use: a. Of universal human interest or use; touching the needs, interests, or sympathies of all men.
b. Having sympathies with, or embracing, all: said of men, their feelings, tastes, etc.; also fig. of things. (Closely connected with 8.)
4. Catholic Epistle: a name originally given to the general epistles of James, Peter, and Jude, and the first of John, as not being addressed to particular churches or persons. The second and third epistles of John are now conventionally included among the number.
It is not certain that this was the original sense of , since some early writers appear to use it in the sense genuine and accepted (see CANONICAL): but the attribute has been understood in the sense encyclical or general since the 10th or 11th c.