I think you're overestimating how significant those numbers say political compatibility is. The study said that 4% of marriages are between a Republican and a Democrat, which *sounds* low, but given that something like 30% of people are Republicans and 30% Democrats and 40% Independents, you would only expect 9% from pure mixing. There are 17% between Independents and non-Independents, but from random mixing you would only expect 24%.
Looking at these numbers actually made me realize that this level of political compatibility appears to be far *less* important to most people than I would have expected. It looks like 16% of Democrats are married across party lines, even though 70% of their options are across party lines (about 1/4) of the expected number), and 84% of Democrats are married to other Democrats, even though only 30% of their options are Democrats (about 3x the expected number) so there's something like a factor of 12 between their probability of marrying a particular non-Democrat compared to their probability of marrying a particular Democrat. But a factor of 12 is much smaller than I would have expected in this era of high polarization - and low enough that you wouldn't actually want a filter that eliminates 100% of the people from the wrong side of that line.
I think you're overestimating how significant those numbers say political compatibility is. The study said that 4% of marriages are between a Republican and a Democrat, which *sounds* low, but given that something like 30% of people are Republicans and 30% Democrats and 40% Independents, you would only expect 9% from pure mixing. There are 17% between Independents and non-Independents, but from random mixing you would only expect 24%.
Looking at these numbers actually made me realize that this level of political compatibility appears to be far *less* important to most people than I would have expected. It looks like 16% of Democrats are married across party lines, even though 70% of their options are across party lines (about 1/4) of the expected number), and 84% of Democrats are married to other Democrats, even though only 30% of their options are Democrats (about 3x the expected number) so there's something like a factor of 12 between their probability of marrying a particular non-Democrat compared to their probability of marrying a particular Democrat. But a factor of 12 is much smaller than I would have expected in this era of high polarization - and low enough that you wouldn't actually want a filter that eliminates 100% of the people from the wrong side of that line.