Wasn't it strange the way the kids could apparently just walk off the street into a professional recording studio and interrupt the session?

First it happened when Greg wrote a song for the kids to record. The producer actually asks the group in the session to stop singing so he can answer Greg's questions.

Later it happened again when Marcia walks in on the Davy Jones recording.

Another time they go onto the set of the talent TV show to ask about performing for money to buy the silver platter, and they talk with the host in the stage area.

Hey it was the early 1970's No security. Until late 2001, people could even walk into a cockpit in an airplane.
So its fairly believable. Security guards are everywhere today including grocery stores, etc. In the 1970s none of that existed and you had much more freedom to roam unquestioned.

Wasn't it strange the way the kids could apparently just walk off the street into a professional recording studio and interrupt the session?

First it happened when Greg wrote a song for the kids to record. The producer actually asks the group in the session to stop singing so he can answer Greg's questions.

Later it happened again when Marcia walks in on the Davy Jones recording.

Another time they go onto the set of the talent TV show to ask about performing for money to buy the silver platter, and they talk with the host in the stage area.
So what else is new?

It probably inspired a lot of irresponsible behavior as kids who watched the show grew a little older, which I think is kind of amusing.