You're treating women differently based on their gender. That's literally sexism.
What's different is the moral color of the sexism. If Eric treats women differently in his workplace because he thinks they should be raising babies, not writing code, our cultural norms say Eric is a Bad Person.
Now suppose Bob genuinely believes women and men should have equal opportunities and career paths in the workplace. But Bob treats women differently in his workplace because he's afraid of a false accusation that ends up with him getting sued, fired, having his reputation ruined, etc.
Then we'd say that Bob isn't a bad person. Or at the very least, he's not anywhere near as bad as Eric. He's just trying to do his best to protect himself from a social system he doesn't control, that will grind him up if he gets caught in its gears.
If you take the definition of "sexism" to be "treating people differently based on their gender," the case against Bob is airtight. Bob's literally a sexist: He treats women differently because of gender.
I think the reason you're trying to argue Bob's not a sexist is because the word "sexist" itself is normative. Sexists are Bad People like Eric. Bob's not a Bad Person, so we shouldn't use the word "sexist" to describe him, because "sexist" has a moral color -- part of the meaning of the label is that you're a Bad Person.
In other words, if you say Bob's not a sexist, you must be taking your definition of "sexist" to be something else. Treating women differently for a certain kind of reason.
With this more nuanced definition of "sexist," it's possible that Eric's a sexist and Bob is not, even if their actual actions toward women are the same.
To properly describe what Bob is, you might need to create a new word to describe someone who treats women differently, but in a morally neutral way (or at least a lighter shade of grey).
Racism might also benefit from having a term that fills this linguistic / conceptual niche. ("Systemic racism" might have fit the bill at one time, but I think that particular term has become colored -- pun intended -- by a moral connotation.)