Catholics wouldn't be any more of a problem than Protestants. The Ruriks intermarried with the Jagilians for example. The brides would be expected to convert. Once she kissed the cross, the Church would never object. Historically, the Russians were rather relaxed in whom they took for tsaritsas.
Uh...the Russians might have been happy had she just willingly kissed the cross, but it's the case of
getting her there to start with. She would need a dispensation from the pope to convert to Orthodoxy from Catholicism, and if the pope doesn't grant it, since why should he, she's for all intents and purposes cutting herself off from "Mother Church" and thus damning herself to Hell (at least they can't be sure she ISN'T doing so). The Orthodox church won't accept her
without the conversion.
Four cases where this was a problem, admittedly all in the 19th century:
Pedro IV/I of Portugal/Brasil who was offered the throne of Greece. He had conditions if he were to convert, and neither the Greek nor the Roman church was willing to sign off on them, so it went nowhere. (Would make for a cool TL if he somehow agreed
without the conditions, though).
Othon of Bavaria and his wife. Neither became Orthodox (he was Catholic, she Protestant), and the palace chapel (Orthodox) had to be de-consecrated for the Catholic/Protestant services and then reconsecrated after the service in the Orthodox rite.
Henri, Comte de Chambord. He fell in love with Elizabeth Mikhailovna of Russia (OTL duchess of Nassau). Nikolai I was willing to allow her to marry him, even so far as to let the Catholic ceremony precede the Orthodox (an inversion of how it
should've gone, apparently). However, Madame Royal wrote to the pope
begging His Holiness to block the match anyway possible. The pope refused to grant the dispensation for Henri to marry a non-Catholic (which would've meant their children would have been illegitimate) and the match foundered.
Hélène d'Orléans. Alexander III (or rather Maria Feodorovna) wanted her for a daughter-in-law. Hélène was game, she'd already offered to renounce her Catholicism to become queen of England. Her father (who was abusive to
all his children) conspired with the Pope to prevent the match by refusing her permission for either.
The only case I can think of where it successfully went through was the marriage of Alexandra Pavlovna and Archduke Josef, Palatine of Hungary, and that solely because she was allowed to remain Orthodox. This isolated her from the Viennese court, which treated her with contempt, refusing to even let her be buried with her husband and stillborn daughter in a Catholic cemetery. So her widower built her a tomb in Budapest, buried her with the stillborn daughter and that was that. And Alexander I had to put pressure on Franz II to allow
that to happen.