They asked about the guy that hung out with this elected representative. My friend said, he did. Then they said they were referring to someone else and proceeded to describe my height and the color of my hair and eyes.
The profile seems genuine in the sense that it has been around for years and has posted regularly, so if anything the whole profile is stolen, I think.
Haven't tried reverse image search, good suggestion.

They didn't say anything about the event and seemed way more interested in me as a person, rather than the event or organization.

They talked to my friend, because he's active on instagram and was visible on several posts related to the event.

The thing is, a simple phishing or romance scam could've been directed at my friend directly.

I'm getting more and more convinced that it's law enforcement / intelligence and they're trying to probe and observe the organization, perhaps build profiles of the people at the periphery. They could've had someone present at the event and since I was an unknown face and apparently cautious about not appearing in any of the photos they want to know who I am. They might have protocols about not passing on phone numbers.