"To feel about someone or something"= "what do you think about this person or thing"

In English, "how do you feel about...?" is simply another way to ask "what do you think about...?" There is really no difference between the two, although sometimes, "how do you feel about...?" is perceived as slightly more intimate than "what do you think about...?" "How do you feel about him marrying her?" = "What do you think about him marrying her?" "How do you feel about the Syrian refugee crisis?" = "What do you think about the Syrian refugee crisis?"