Yes but it's not binary, its hexadecimal and something we can't fathom so lets "move along" like a great sand trooper once said

No it’s kinda like Dark matter we know it exists it’s just hard to prove kinda like the force.

Does magic have a gender? does Fate? what about destiny? Does life have a gender? does death?

Answer those questions and you shall have your answer

How would a source of power have a gender?

It's a field of cosmic energy that permeates throughout the entire galaxy, gender is not a concept that applies

Interestingly, the different aspects of the Force have genders: the Dark Side is male and the Light Side is female, per the Son and Daughter existing

Although that's probably just a manifestation of a need for an explanation that makes sense to regular living beings

How come something that binds every living thing in the world have gender? If course it doesn't have gender

^^The way that the dark side is male and the light side is female is also seen in the dyad.

Although, shouldn't the Father be non-binary in that case?

^ In Legends there is a step-Mother.

^^The light and the dark are the two simplest parts of a cosmic construction as Lucas said. In this sense, Star Wars uses a reversed Yin-Yang with a touch of Christian Trinity.

The light is creation, day, femaleness in the world of forms, and within beings it is selflessness, compassion, fairness, charity and hope. The dark is destruction, night, maleness in the world of forms, and within beings, it is selfishness, greed, fear, anger, hate, bitterness. Rather than being a binary system, everything is the mosaic of both light and dark, each and all containing the seed of the other, making up all aspects and phenomena.

The Daughter and the Son born out of of these forces, as living beings, but they are also subjected to the influence of both light and dark (the Son can become greedy, the Daughter can destroy) and they proceed from the Father, who represents unity behind the duality, and they ought to manifest his will, that is a balanced interplay of the two forces. I assume, it's a "he" because of Lucas' Methodist upbringing (every time I saw him referring to his concept of God in interviews he always refers to it as "that" instead of "he," but apparently he likes the idea of the impersonal Force manifesting itself in the universe as a Father).

I personally always imagined it to be genderless because it’s also not really a actual physical creature. I’d like to imagine the force as an otherworldly being that is sentient, and at the same time it doesn’t have a body or anything you can actually physically touch or feel