If you see them as people, you should be able to interact with them as fully-rounded people, including asking them out (once only, not being a persistent nagging asshole), complimenting their attire, telling them the latest gossip, in short - communicating your feelings, provided the feeling is mutual. Whereas in a professional setting, you aren't a person, you're filling a role and obeying protocol. It's a sliding scale between "professional" and "casual", but generally when you're interacting professionally, you aren't addressing the full person, you're only letting your Senior Frobnicator part discuss frobnicating barbazniks with only the Chief Barbaznik Wrangler part of the person in front of you; whereas in a casual setting you're communicating with all parts of the person.
This might be the best summing up of the/our schizophrenic attitude towards professionalism (and work) that I've ever read. The words, "in a professional setting, you aren't a person," just nail it. Meanwhile, the corporation itself has the legal status of a person, and can now even claim to hold religious beliefs. Ergo, we could probably fix some of these issues in the valley with a few properly Gorean S Corps.