Asimov did write female characters but they are rare. Two that stand out are Susan Calvin (in the Robot series) and Noÿs in The End of Eternity. Calvin is described as follows: "She was a frosty girl, plain and colorless, who protected herself against a world she disliked by a mask-like expression and a hypertrophy of intellect" [0].
The main exception is The Gods Themselves, which is notable for discussing sex, albeit in a tri-sexual alien race.
[Edit - to be clear, this is not intended as a negative judgement of Asimov against today's sensibilities. Slightly reworded accordingly]
To be fair, Asimov didn't really tend to write very character-focussed fiction much, his male characters were generally no more developed than the female characters; protagonists were mostly lenses through which to explore the tapestry of broader systems, while non-viewpoint characters were mostly low-detail elements of the scene, he was more interested in showing the forest than lavishing detail on individual trees.
You are right about Asimov's style, it hasn't aged great. But he was an intellectual at heart, so his writing fits his personality.
People who need their author/actor/etc to be exactly like themselves are probably racist.