women were considered inferior,
Not in BM, obviously. This convention just does not exist in Battlemaster.
Well I am racist with my friends,
Probably the 'play as if you were with your friends' comment was meant generally, not as a literal direction to behave in BM however it is you behave around your friends.
, and racism was an open reason to go to war.
Not so much. Religious differences were a far bigger reason. Not to say there was no racism, but you did not have lots of races all in the same place very often. You did have neighbors who were heretics or heathens, and if it so happened they were a slightly different color, that would help - but the Vikings did not invade Saxony or England because Saxons weren't vikings. They wanted loot. The reconquista did not happen because white people didn't like brown people; it happened because Catholics couldn't stand losing the whole of Iberia to the moors.
If we all start playing as if everything was all fair and equal back then
I don't think that any serious argument has been made in favor of applying 21st century egalitarianism to Battlemaster. The only real change in the rules is the consideration for women in combat, which is big but fairly easy to make.
Other races were often feared and hated, just because they were different. Gays could be stoned in the streets, bastards were often left to die or killed, underage girls were often married and were having sex around the ages of 10-12, and women were often seen as second class citizens.
This is all true but to hand this kind of ammunition to amateur writers and RPers is to ask for an internet clusterf*ck. To address these topics requires a certain degree of sensitivity and also extensive knowledge of how and why they occurred in the Middle Ages. In the right hands, it could be insightful or revealing; employed as a bludgeon against another character you don't like it's just the lazy way out in the same way that graphic sex and violence on television are often the lazy way out. You have to know the rules before you can break them and while I would applaud a serious attempt to play a character as openly gay, it'd be a very difficult exercise and with so many pitfalls for players rather than characters to go from 'hey fun battlemaster escape' to 'augh modern day bigotry' that I'd just as soon go without.
Frankly, I'm impressed when people bother to spend a few minutes learning about medieval politics or society. That you're aware of a generalized medieval bigotry does not arm you sufficiently to write it into your character in a meaningful way. Maybe you can (I don't know you) but it's hard for me and I've been at it for a while.
On a more historical note, I would also point out that much of what you describe did not go without complaint in the middle ages. The church was tremendously corrupt but your average, everyday person was no more comfortable with the idea of a ten year old getting married than we are today. In a noble family where heirs could mean war or peace you might jump the gun as soon as the girl was capable of producing offspring, but I would be careful about overgeneralizing how bad things were. The whole reason that people put up with the corrupt Catholic church is that they did not want a return to the Dark ages when there was really no authority at all to stop this sort of thing.