These tears aren't about pride, they're about the release of emotional energy. When long-standing walls come down the sudden release of emotional energy can motivate tears. I think many of us have walls to protect us from people we think will be of harm to us in some way. Bigots protect themselves from the "others", and we in turn protect ourselves from them. When they drop their guard, it may motivate us to drop ours, and release happens on both sides.
I cried because I live with silly assumptions about people - assumptions like "world war II vets don't like homosexuals". It must have been a subconscious assumption, one created by my associations with family and friends who are much like this man but who hold different views. When I heard his speech it must have pushed at that wall and it came down. I cried.
You're a fool if you think by denying what we feel we become, in some way, better men. It's a painful mental state that will target your own feelings and behaviors as much or more than it will others.