When you have an array of possibilities that you can belong to, such as different races or nationalities or what have you, and belonging to any of them doesn't put you at any advantage in terms of salvation compared to belonging to any other, and there are no moral implications to the fact of which one you belong to, then they are all equal. All races are not equal because of some feel-good filth about being nice to each other. That's garbage. Specifically what makes all races equal is the fact that membership in any one gives no advantage in terms of salvation and the fact of which race you belong to has no moral implications. That's what actually makes all races equal. The very same applies to all nationalities and both genders. Belonging to any gives no advantage in terms of salvation.
Now, each race and nationality has its own culture and identity which cannot be diluted and no one can be forced to accept the culture of another because each race and nationality has its own unique individual dignity that cannot be trampled on because of another race or nationality. That means that not only is White Supremacy evil, but so is Black Supremacy. Equal means equal. That also condemns Russian Supremacy in Eastern Europe, which is not only alive today, but continues back clean through Soviet times and all the way back to Imperial Russia. Racism and nationalism are both still very real problems in Europe. We are all, by our human natures, called to each reciprocate Christ's love for each of us. He is the one we laud as the "Lover of mankind". This is what unites us. Racism and nationalism divide us and thus impede Christianity and that is specifically why such ideologies are wrong.
Similarly, each gender also has its own unique individual dignity, yet both are still simultaneously equal according to what we said earlier. Promoting either gender acting like the other destroys that gender's dignity. Each gender has it's own role to play and the fact that they have contrasting strengths and weaknesses is specifically designed to make them complimentary, not rivals or to destroy their own identity and dignity by acting like each other. This is more of a "ying and yang" situation than races and nationalities, but with equality simultaneous to individual identity and dignity in the same way.
However, the array of possibilities that is radically different from the ones we have seen here is that of sexualities. It took me a while to get to this point, but astute readers still saw it coming from my opening sentence. While what race, nationality, or gender you belong to has no moral implication and none of the options present any advantage over any other, what sexuality you practice most certainly does (for that matter, this part applies equally well to what religion you practice). There are moral implications to what sexuality you practice and human sexuality does bring you closer to God, using what God gave you for the purpose for which He created those things, and deviant sexualities, be it lustful heterosexuality, sodomy, bestiality, whatever (it's all lust in the end), separate you from God, refusing to use what He gave you according to His plan for you and instead following your own plan following your own happiness. That does separate you from God. Being Black or Ukrainian or whatever doesn't mean you are separating yourself from God by being that way. Such realities about yourself do not impede or accelerate your salvation and that's what makes them all equal. Rejecting the plan for which God created you in favor of your own emotional and physical pleasures is self-imposed separation from God. When people live that way, it's just sad. When they respond to admonishment (which is a work of mercy, btw) by hating you and calling you names like "bigot" just because you don't agree with their personal emotional pleasures, it's even more sad. You can't help but feel sorry for the arrogant and selfish people in the latter category. It's a real shame... ...and when you realize that God created all of them to be saints...that reality is just depressing.
If this counts as "hate", then you desperately need a new definition of "hate".