And even EUIII realized that interfaith royal marriages didnt happen.
In 1299, Bey Orhan I, of the Ottoman Beydom married himself to Helene(Nilufer) Hatun, supposedly the daugter of a Byzantine provincial overlord and again in 1346, to Theodora Maria Cantakouzene, Princess of Byzantium and daughter of the reigning emperor Ioannes IV Cantakouzenos. Neither marriages involved the religious conversions of either ladies.
Orhan I had a son with Theodora, who could have been a contender for both thrones, named Halil. It was even arranged for Halil to marry a daughter of Ioannes the V's and Orhan I was actively nurturing him for the Ottoman throne. Too bad Orhan I died a bit too soon, and his eldest Murad I(ironically Helene's son) took the throne by force. When young Halil tried to claim the throne, his elder brother had him executed.
Anyway, this pretty little tale might be proof that such marriages could take place when there was suffiecient political interest behind them on both sides. It's what a lawyer would call precedent i think. So i would humbly suggest that the whole issue of religious incompbatibility be put to rest. There must be a million other important reasons why a Russian Czar wouldn't marry a Chinese princess.
I can hypothesize of a couple situations where a Russian Czar would find it in his best interest to pursue such a union. To strike an alliance against the Japanese? Or at least secure some sort of peace on the massive land border he shared with China, at a time when his attention was required elsewhere? I really couldn't tell for sure and other people seem to have some ideas on the matter that are interesting.
Of course, the matter of whether either or both parties would rush to acknowledge a male heir produced from this union as a viable claimant to their throne, is a whole different story...