what was required for non-Catholics to marry in Francoist Spain? Imagine, for example, that two Protestants want to marry in Spain in 1950
Short answer for 1950: they needed an affidavit expressing that they were not born catholic or the testimony of a protestant priest recognized as such by the Spanish State.
Long answer for the whole of the Francoist period (1936-1977):
1- 1870-1931. Legislation existed from the time of the parliamentary monarchy in Spain that gave legality to civil marriage "outside of Catholicism"
This law established that Catholics should marry within the Catholic Church, and that in all other cases (protestants, muslims, mixed marriages), the contracting parties should make a statement not to be Catholic. No further tests were required.
2- 1931-1939. This legislation was greatly expanded during the 2nd Spanish Republic (1931-1939) giving full freedom to civil marriage.
3- 1938-1941. The Francoist government at first recovered the legislation of the monarchy. He did this very early, in 1938, before the end of the Civil War in 1939. In theory, the Francoist "Bill of rights" aknowledged marriage as a fundamental right for every religion.
But the civil marriages contracted during the Republic only were valid if the contracting parties were not Catholics. If the spouses were Catholics, they were obliged to remarry within the Catholic Church, but the effects of marriage were retroactive ("sanatio in radice", according to the Canonical Code of 1917, a Vatican, not Spanish law). In fact, civil marriages inherited from the Republic had many practical problems, too long to fully detail here.
4- 1941-1951. Later, in 1941, the law was hardened. Civil marriage became a system of last resort, if not second class, and the contracting parties had to prove that they were not Catholics with the testimony of a Muslim or Protestant priest or other type of evidence that could be very difficult in the case of exotic religions. Atheism was not accepted as a motive for civil marriage. Not having been baptized as catholic was accepted: the declarant had to make an affidavit and the consequences if it was discovered that he lied could be serious.
5- 1951-1967. The law was further tightened in 1951 by the signing of the Concordat with the Catholic Church. Since then, only the Catholic Church could prove that you were not Catholic. If it took time to provide the evidence, you had to wait. The Church's willingness to help non-Catholics to marry was not always great. In practice Muslim marriages were protected by the state and had no problems if people to marry were both born Muslims.
6- 1967-1977. In 1965 the Catholic Church became much more liberal with the Second Vatican Council, and this was reflected in a Spanish law of 1967. Since then, a declaration of not being Catholic was enough.
Franco died in 1975. Civil marriage did not have full equality in Spain until 1977.