I've seen both and honestly don't think nominal dues themselves have anything to do with involvement (or lack of) in most cases.
The reason I don't think it has an impact is that once you get past the membership drive and perhaps a very few perks of membership, it doesn't matter.
The elementary school situation is the simplest since the parent group is THE central organization. Once you get into secondary, it's more complicated for many reasons.
In our elementary, we charged nominal dues. Paid members got a school directory for free (cost was equal to or more than dues) and could hold office. Otherwise everyone was the same. No one had to be a paid member to come to a meeting or volunteer or attend an event. Benefits we gained by charging dues:
- Forced us to have a membership drive each year and really market our organization. This meant we had discussions about it in our meetings, developed material/posters about benefits.
- Subconsciously, people sometimes perceive "free" as "low value"
- Filling out the form/writing the check was the first step in commitment and getting involved.
- The membership drive included a contest to see which class could get the most members. This involved the students and got them excited about PTO.
- It did give us some additional funds
You could actually have many of the same benefits without charging. Still have a "membership" drive even without fees and get people to fill out their contact/volunteer forms. But the problem is - there are so many things to do at the start of the year, it's too easy to say "why bother since everyone is already a member".
We've seen far drastically reduced participation in middle and high school. But interestingly enough, PTO was "free" in middle school. We usually had 4-8 parents involved (about 900 kids). The high school has a PTA with $10 dues and far more competing organizations. It's still small, but I think we have about 25 attend monthly meetings and 80-100 paid members. (School has 1900 kids).