No, men are not all part of Man Club, where we meet up and agree on how to co-ordinate our movements to enforce the superiority of men over women. In fact, closer to the opposite is true. In a capitalist, democratic system, we are very competitive.
No, men in power are not concerned with the well-being of men as a group. They are concerned with their own well-being. The existence of male leaders does not mean that no men are oppressed. Male leaders have typically been happy to let other men suffer for their maleness, as long as the leaders are themselves spared. They are happy to apply double-standards to others, if those standards will never be applied to them.
Rich, powerful adult men are going to endorse male genital mutilation. They aren't at risk of being mutilated. In fact, if it gets them funding and popular support, endorsing this practice is actually in their material interests.
Male political leaders have always been happy to endorse a gender-specific draft. They can send men off to suffer for being men, because nobody is going to sendthem to war. The endorsement does not put them at risk, and in fact opposing it might jeopardise their political career. They look to their own interests, not to the interests of men as a group.
Men as a group are individuals. We do not form a collective hive-mind. These are just two examples of how the existence of male leaders does not mean all men are safe. It would be just as ridiculous to suggest that the existence of black leaders means that the oppression of black people cannot exist. It's the apex fallacy. A majority of those enjoying the benefits of power are men, but a majority of men are not enjoying the benefits of power. It's something that a lot of people confuse. Although I can't say anyone should care about being trolled by a male feminist, after all they are just a much larger fail version of a feminist, and in the case of manboobz is actually literal and figurative.