How did I test: I made a household of 8 sims. Every one was a clone of the first one with the only difference being their star sign. Then I put all but two of them in a locked room and saved the game (by saving there, it was all one game) Then with needs set to static, I got the two remaining sims to go through a series of romantic interactions starting with asking the others sign. When I got them to marry, I reloaded the game and picked another couple. Each couple went through the same list of interactions in exactly the same order (with the exception of a few cases where one or two interactions were not available) I kept doing this until I had tested every possible star sign combination - I had to do it with a few different households.
I kept a record of where in the list each couple became romantic interests and where they finally got married. Generally the compatible signs became romantic interests a little earlier then other couples and said yes to marriage earlier. The couples that were incompatible still became romantic interests, but would not marry - maybe if I had kept at them they might have married, but I had a list of close to 100 interactions that I had tried where usually the other couples were married by about 35.
I did a number of the combinations twice and even three times to be sure of the results and that's when I found the incompatible ones were random.
As for in-game checking, it seems all you can do is ask a sim their sign. Then it will say "sim 1 learnt that sim 2 is a scorpio. The signs are compatible" or just "sim 1 learnt that sim 2 is a scorpio" Couples that are compatible are always compatible, but when it doesn't say they are compatible, there is no way to know in advance if they will be incompatible.
Norma