If your parents decide to donate to Barnard, don’t do it for any perceived benefits - have them do it because they truly would like to further the school based on your experiences there.
There’s no reason to join any parent organization.
Yes, in theory there will be “by invitation” events, guest lectures, etc., where they might rub shoulders with the college president, deans etc. - but in practice it won’t affect your own time at the college.
Actually, the college is “small” enough that you personally will often run into president Sian Beilock, deans, etc. - everyone is quite visible.
My daughter ended up with one of the deans as her adviser (as she was covering for someone temporarily), and frequently ran into Sian in her apartment building during Sophomore year.
After I saw how they were handling Covid and how they worked to support low-income students who had been depending on campus-work, I did end up making very modest donations each year — but never joined any formal group.