I have been propositioned for this kind of thing in a business context and have refused and not had negative blowback from doing so. That was actually the first mental shift I tried to see if it made any more sense to me that way, but it still seemed overblown. I can't think of an invitation that it is socially acceptable to make to a new acquintance that it is not socially acceptable to make to a new potential business contact, admittedly I guess that might be a consequence of the extremely limited array of things I consider to be socially acceptable invitations to new acquaintances.
Just saying no thanks is really not so hard, and if it continues after that point it becomes a hell of a lot less ambiguous or defensible.
This is not to say this is absolutely positively an instance of either of the above, merely that it is too ambiguous and unclear to not come across poorly.
The question is: is taking someone's business card under the auspices of a business inquiry and then using it solely for your own personal reasons unprofessional or not? The answer (I'll go out on a limb here...) is: yes. It's unprofessional. Interesting point, blog author! Thanks!
Whether or not you think women are treated unfairly in the industry (I used to bristle at the idea, then watched my wife interview for jobs and radically changed my take), and whether or not this particular woman endured any real unfairness:
It is still worth considering how totally unprofessional and inappropriate it may be to ask a woman for her business card in order to abuse it for your personal benefit. It's not something I had thought of before. It's worth discussing.
If gender politics makes your brain turn off (and, it used to do that to me too), just pivot the story in your head so that instead of asking for a date, the guy takes her card at a tech convention and later calls and tries to sell her a dental insurance policy. It's spam. Spam is bad. There's an implied agreement when I give you my card that you're going to use it for its intended purpose: to contact me about something relevant to my business.