100% of the trips I take alone, I cry. As you've said, it's beautiful and freeing. Sometimes it has to do with insights (There is nothing to worry about, I *AM* happy, I don't have to do anything or go anywhere to be it, I AM already it). Sometimes it has to do with me watching movies/series (usually Twin Peaks, most lately Interstellar) which are heart-wrenchingly pure. Also, reading "Be Here Now" does it every time. "Unless you become as little children, you cannot enter the kingdom of heaven." Aaah, the total purity.
4HO-tryptamines (my favorite psychedelics) bring it about so elegantly.
I've never cried during a trip with other people, the only exception being trips with my girlfriend. Also, 100% of those trips. I'm 30 and she's 23, and the way she holds me in those intense moments signals to me she's a very old and compassionate soul.
Before I tried psychedelics I never cried (unless maybe once or twice caused by a breakup - although that were cries because my ego was hurt, not because my soul was touched).
Bottom line: tripping learned me crying is equally important as laughing. Doing it without judgment feels absolutely freeing, as you've put it so adequately.
At this moment, I can cry even without psychedelics (I consider this a big step). Sometimes I can't, and that means I've got work to do (removal of blockades, mostly).