This is kind of a tricky question that involves aspects of politics, diplomacy, economy, and obviously social, cultural and racial issues, but let's cut it short: would it have been possible, given the circumstances and the time, to have a Modern history nobility (16th to 18th centuries) in which the intermarriage between Christian/European royal/noble houses and Eastern/Non-Christian royal/imperial/noble houses could be a common or uncontroversial thing?
When I mean Eastern, I mean not only far-Asian nations like Mughal/Maratha Empires in India, or the Empires of Japan and China, the Kingdom of Great Joseon and so on. Eastern Orthodox Kingdoms like the Georgian Kakheti/Imereti were largely ignored by the rest of Europe, even Russia took some centuries to be culturally and diplomatically absorbed into the rest of European royalty. The Ottoman Empire (yes) could also have been an option if great European powers felt the need to forge an alliance with their main rival. Maybe even Sub-Saharian African kingdoms could have had their place amongst the marriage market.
But I want to know what you think about it, if it is too much of a stretch or if this could've been somehow possible. If not, how to make it possible? I wait for your answers.