Exactly! Talk to them like they're a person. It's not that hard.
You'd be surprised how refreshing women find it when you talk to them like they're a person, not a "woman". At least based on what they've told me when I took that approach. Maybe they lied ¯\_(ツ)_/¯
The idea is that you treat them like people, not like a bag of stereotypes.
I think it might be a bit presumptuous to think that a woman who feels she needs to be cautious just needs to have a contentious guy talk to her, as if she and her presumptions are a puzzle, and being contentious is all that's needed to solve that "puzzle"
As to the question of, "Well, if she's going to be guarded about everything, what do you say?" -- in the context of the current thread, my opinion is that it is nothing about what you say, but the context and setting. Don't ask her what it's like to be in a boy's club or similar small talk while she's working at her desk. Go out for coffee, and bring along another co-worker or 2, if the intention is to make a new worker become acclimated with the rest of the company.
Treat them like they already belong.
As for it-might-look-like-a-date ... ask them to tag along for your mid-day coffee run. Don't ask them out for coffee on a Friday evening.
There's a formula for this kind of thing, but polite professionalism is also a communication skill that needs practice. The formula goes like this: 1. State why you're about to ask for whatever it is. 2. Ask for it.
Assuming #1 definitively isn't "to get a date with this person," then it's really quite straightforward to handle the situation. If they imply that they think you're making some advance, you can literally say "No, wait, I think there's some misunderstanding, I'm not doing that, I'm literally just [repeat your reason for talking to her]." And then make some concession to demonstrate the point, such as "If this would make you more comfortable, we can discuss this out in the common area."
If it's a casual conversation without a strong agenda, you can also just say that. "I don't really have an agenda, but I want to get a sense for your communication style so that I know how to work with you."
I'm with you, treat 'em like they're people. And quit distinguishing them as different, like TFA.
We are slowing emerging from millennia of patriarchy. Insisting on pretending otherwise doesn't sound like treating people as people to me. It sounds like insisting that they conform to your expectations, which I think is pretty much the opposite of treating them as people.
Work doesn't need to be about buddies. work is about work. That's why you have a personal life. keep the two separate.
corollary #1: dear manager. I am not your friend, you are not my friend. i will never be your friend. Chances are i don't like you at all. Just be professional, and i'll be fine with that.
I am curious: Are you going out for lunch alone? Or are you not going out for lunch at all? Or don't you have a lunch break?
Realistically, the conversation can go something like "hey, i'm going to the break area for coffee, wanna come?" ... "So how is your work going?" ... "Huh, that sounds ... Anything I can do to help?"
If you're completely risk averse but still want to be a supportive male, you can have this entire conversation without bringing up that they're a woman.
Alternatively, If you want, you can make a passing comment, maybe with a joke, like, "Just wanted to check in because engineering can be a boys club sometimes. Want you to feel like you're in the club." Maybe you can say "It's a little dorky, but I read this interview where a female engineer suggested talking directly to women about their experiences and it seemed like a good idea. I just wanted to see how this job is treating you."
As long as you don't leer while you say any of this, everything will be fine.