Do Muslims believe that the gender inequality and criminalization of homosexuals by Muslim countries is justified?

No I do not believe it

Islam says men are superior [in terms of strength] and have been given the responsibility to provide and protect women. This doesn't mean that a woman is of lesser value, though. This is your own false assumption. Islam says both righteous men and women are rewarded equally. Women aren't rewarded "less" for the same deeds as men. Etc.

Let me tell you what I see when I look at free, Western society. I see women prancing in front of men as if they are pieces of flesh to grab on to. I see women leading unhappy lives in a career climb that doesn’t satisfy their natural instincts of being a woman. I see women stuck in miserable marriages with men who take them for granted, and who often leave them for a younger “chick,” or cheat on them. I see one out of two marriages ending in divorce, if not more, and who knows how many other unhappy ones. I see women who seem to have attained “freedom” and “emancipation,” but come home from a long day at the office to still do 90 percent of the housework. I see women in this free society who hit the glass ceiling far too often because they are women, and I see that those who succeed often have to drop every iota of their femininity in their climb up. I see women who are free to wear whatever clothes that they choose, yet parade around wearing as little as they can to get whatever recognition from the opposite gender. I see pregnant teens. I see teens who’ve lost their innocence before they could even understand what having any kind of relationship is all about. And all this, I see in our “free” society. A society that supposedly recognizes women and treats them with some degree of respect. My point is—what appears as freedom, isn’t always so. What appears as “women’s rights” can also lead women to the most degrading, self-humiliating behavior lacking any self-respect. Unlike the Qur'an that you Non Muslims describe, the Qur'an that I know takes a balanced approach, bringing out the true essence of every individual, while respecting the uniqueness of both genders and setting parameters so that this boundary is not violated. I wish that just for a short while you would be a part of a practicing Muslim community. I think you would be surprised with, for the most part, the degree of respect the women are given. You would hear the men speak about the greatness of their women. You would hear the Imams words quoted about the higher spiritual source and level of women, about the strength of Muslim women, about the vital contribution of the Muslim woman. But most of all, you would see husbands and wives working in partnership, looking at each other with respect, each doing their own part to bring more Godliness into this world.

Yes

Allah swt knows best. If his Sharia Law says that we mustn't then yes, we Muslims believe in criminalization of homosexuals, but no we DO NOT believed in gender inequality, as in the Quran it says, both women and men are equal in the eyes of Allah swt.

Islam gives us different rights to males and females, the gender is unequal by default, hence why it is called gender dimorphism.

But spiritually they are equally potential and legally they have weighted rights which is best suited for either genders.

Homosexual relations is a crime yes, and also to carry out homosexual propaganda, but there is no incrimination of those who don't act on it and remain celibate. Homosexuality is equal to corruption of God's law and therefore there can be no islam with violation of islamic rules

They certainly should.

i dunno, ask a gay muslim