There is major confusion on this question. In one sense, yes, of course Muslims accept the principle of equality because that is at the essence of all morality. How so?
Implicit in any and all moral systems is that two like things ought to be treated equally. If Person A shoplifts at a grocery story and we judge that as wrong, then if Person B does the same thing, we should also judge that act as wrong, all else being equal. The “all else being equal” part is important because, in one sense, Person A and Person B are *never* equal for the simple reason that Person A and Person B are two different people with different circumstances, different backgrounds, etc. What is important from the standpoint of morality, however, is that Person A and Person B are equal in a relevant way and there are no differences that are morally relevant. For example, if Person A has green eyes and Person B has blue eyes, that is not morally relevant to the fact that both men have committed theft, so we will treat them as equal before the law. But if Person A is a millionaire and Person B is a starving homeless person, then that is a morally relevant difference and we should treat and understand Person B’s actions differently.
What we learn from this is that our notion of equality is highly dependent on these “morally relevant factors.” This is important because people nowadays look at Islamic law and say, “Look at how Islam treats women and men differently! Clearly, Muslims reject equality!” Some Muslims unfortunately also make this mistaken assessment.
In reality, however, Islamic law recognizes that there are, in some circumstances, morally relevant differences between men and women. Given that men and women are in actuality very different in certain respects, it would make sense that there are scenarios where those differences would, morally speaking, come into play. From this perspective then, it is not Islamic law that is unjust and oppressive but rather any system of morality and law that ignores these differences.
Furthermore, cheering for and rallying behind the notion of equality, as liberalism does, as if they discovered the concept, is so silly and vapid. It’s like you’re congratulating yourself for something that literally everyone else has. Again, equality is implicit to normativity itself. Where moral systems differ is how they understand and define those morally relevant factors, and that is a discussion that happens on the meta-ethical and metaphysical levels. For example, instead of pointlessly debating meaningless questions such as whether liberal secularism respects the principle of equality more than Islamic law does, why not debate what an ideal human life looks like? Why not debate what human flourishing entails and what an ideal society consists of? These are the real questions that will, among other things, illuminate these morally relevant factors. But liberal secularism, while hiding behind empty slogans of “freedom” and “equality,” says these questions are irrelevant, that people can decide for themselves and that there is no right or wrong answer. This, of course, is nonsense.