I think giving every character a male or female marking is a bad idea. It would be kinda frustrating to go through all the trouble of making what you consider a beautiful character only to have them with a garish pink symbol on their haunch. Also, there are inevitably going to be people who simply do not want to have their on gender displayed, or who will have characters they don't consider to be male or female. It might be better to display a female or male symbol along side the character name. Also, people should definitely have the option of opting out of choosing a gender symbol for their character, and displaying the gender of others' characters. Alternatively, it could be automatically displayed on the bio (again, people should have the option of not choosing a gender).
I think that the problem lies mostly with the people who get offended when asked their character's gender, though. They are the ones being unreasonable; there is nothing offensive in the question.