There is at least one part where gender is unambiguously important and central to the plot and where if you pretended they were all women, it wouldn't work.

Also, more generally, the genders are definitely part of Tolkien's intent. Like, he's writing a fantasia based on texts that are gendered, and he inherits the gender from the source material. It's not strictly speaking incidental. It's possible to imagine a female LOTR but it certainly isn't Tolkien's LOTR.