I have never had white clots, but I do get dark red ones all the time. I used to think that one of those clots held an unfertilized egg. But I recently read that there is an anti-clotting factor in your uterus during your period that allows the blood to flow out. If the blood gets backed up trying to get out (like a traffic jam on heavier flow days), it can start to clot in your vagina. This is normal and, yes, it is gross. Really big clots can be a sign that your flow is too heavy, but only your doc can tell that for sure. I get them more if I have been sitting for awhile and stand up, but I don't know much about the shape or orientation of the uterus part. I do know that mine is tilted, but I was told it shouldn't cause any problems.
Total abdominal hysterectomy at age 26 due to abnormal bleeding. Kept ovaries.