If you're not going on a work dinner with female employees because of what you describe, but do with male employees, then you are discriminating.I agree with you that it sucks. I disagree with the idea that male managers are wrong to be hypersensitive to the optics of their interactions with subordinates and especially with subordinates of the opposite gender.
Boundaries are either a critical consideration in the workplace or they aren't. If boundaries are indeed critical (A sentiment I agree with), then managers can and should take precautions to avoid even the faintest appearance of impropriety in the workplace. This is especially true in the United States where we basically have the least employee protections in Western civilization. Avoiding the appearance of impropriety means identifying workplace relationships that have been historically abusive and doing everything you can to avoid creating that situation for your subordinates or yourself.
I'll give you a real-world example that I went through to explain why. While I've never been accused of sexual impropriety, I have been falsely accused of a discriminatory termination because I terminated an employee of a different race for wage theft. What the employee didn't know was that I had incontrovertible evidence captured from system logs I'd used when I had previously terminated others for the same crime. The employees in question were signing into our time system and clocking in from home (Initially evidenced by consumer IP addresses that were not even remotely close to being associated with our ISP or internal subnets). I could see within the surveillance systems that they were either a)showing up well after they'd clocked in or b)not bothering to show up at all. Despite that evidence, there was an investigation by HR. I was vindicated but that didn't make the process any more enjoyable. I should have taken my findings to HR first and did in situations after that occurred.
In the specific context at hand, you have to ask yourself uncomfortable questions that people may not understand unless they're in that position. If I ask a female subordinate out for a working dinner, is she going to take that at face value or assume I have underhanded motives? Is she going to feel compelled to go even though she doesn't want to? If she goes but didn't want to, will she resent it? If she declines, is she going to assume that a less-than-stellar performance review down the road is related somehow? If she feels it was all benign and coincidental, will she discuss it with a friend who went through a terrible situation of her own and convince her that her impressions were wrong? If an accusation flies, how much evidence do you have to prove your intentions were professional? Would you personally think the risk-reward equation justifies putting yourself out on a limb like that?
If you're a male manager and have any sense at all, you should be asking yourself these types of questions when you interact with a female subordinate precisely because women in the workplace have been mistreated and may interpret your actions in a way that you don't intend. Being aware of that history can influence your decisions every bit as much as being oblivious to it.
If this, in my opinion, irrational fear that you have changes how you interact with female employees, then you should also change how you interact with male employees