When you think of an eldritch horror, or an old god, do you really consider what their fucking gender is?

Absolutely. Gender has been an important part of Western fiction, history, and dialect for literally centuries, if not millenias.

In Judeo-Christianity and most European portrayals of it God is often portrayed as a male. Have you not seen the famous painting "Creation of Adam"? Or how Jesus himself is portrayed as a man?

That is to say if God is gendered, then nothing is off limits.

Now, to address your question "should we gender lovecraftian horrors?"

Yaldabaoth is a man, often portrayed similarly to Nicholas Tesla, a male Pharaoh, and sometimes Adolf Hitler himself.

As for other Lovecraftian horrors? Yog-Sotthoth (the spaghetti kaballah) is a man. From Lovecraft himself:

Yog-Sothoth knows the gate. Yog-Sothoth is the gate. Yog-Sothoth is the key and guardian of the gate. Past, present, future, all are one in Yog-Sothoth. He knows where the Old Ones broke through of old, and where They shall break through again. He knows where They have trod earth's fields, and where They still tread them, and why no one can behold Them as They tread.