First, you need to actually understand what passive-aggression means and what behavior actually constitutes PA, so, don’t take my word, take that of a peer-reviewed journal in the field of psychology:
psychologytoday.com/basics/passive-aggression
Psychology Today is not AFAIK considered a peer-reviewed journal. It certainly wasn’t allowed as a reference for any research paper when I got my psychology degree. In any case, I didn’t see a definition of passive-aggressiveness in the link you posted, and I’m not sure what aspect of passive-aggressiveness you think applies here. There is no covert anger (which is the basis of passive-agressiveness) that I can see in the situation, and there isn’t that “agreeing to do something and then quietly not doing it” which is the epitome of passive-aggressive behavior. Unless the note was nasty or abusive or something, which the OP didn’t say, there isn’t any evidence of anger at all.
Conflict avoidance is not the same as passive-aggressiveness. But this isn’t really the place to debate psychological terms, and I’m sorry I started it. However, the term tends to get over-used, and a lot of people think they know what it means and don’t (I mean people reading the accusation of passive-aggressive behavior, not necessarily people making the accusation), so it doesn’t convey information in a very helpful way. Communication only happens when both sides agree on what the words mean.
My real point is that there is no evidence that the person in question is behaving in an awful or presumptious way, or that they had any hidden motives, or that they knew what the right thing to do in the situation was. When you consider how many Catholics don’t even understand the true meaning of the Eucharist, it seems likely that there are lots of Catholics who don’t know how to contact the Parish Council, or whoever’s appropriate. The only obvious person to contact would be the person playing the music, but it’s hard to see how you could talk to them directly without hurting their feelings. The person who left the comment may have even done something like, “Well I’ll leave it in the pew, and then if the Holy Spirit guides someone to read it, then He does, and if He doesn’t, it wasn’t meant to be read.” I’m not saying that the person is in any way right in this assessment or tactic, just that they may be well intentioned, and charity requires us to assume the best until we have some evidence otherwise.
It’s just that I could see in my imagination, some shy person, maybe an older person and/or one with less-than-perfect hearing, feeling strongly about how it was distracting and harder to hear the Gospel with the piano playing through it, and not knowing what to do about it, and just writing the note something like a message in a bottle–leaving it to God or to chance whether it gets read. Sometimes people who are hard of hearing become very diffident about it, like they don’t really have a right to complain about having a hard time hearing things, because they feel (incorrectly, of course!) that it is somehow their fault that they can’t hear.
Admittedly, it is an imaginary person I am describing (although I know some people who could behave that way), but so is the proud, cowardly, passive-aggressive person trying to get someone else to “do their work” that others are describing. Maybe the complaint was nasty or insulting or something, but the OP didn’t say it was, so I’m assuming that it wasn’t.
And I admit that I am unavoidably biased by the fact that the complainer was right, and people shouldn’t be playing music during the Gospel.

I think (hope?) my analysis would be the same even if I disagreed with the comment, but I am a sinner, so I can’t guarantee it.
Anyway, it’s fine to ignore any comment received anonymously if you want to. But you do it because that is the established procedure, or because the comment requires explanation that you necessarily can’t get from an unknown person, or some reason like that, not because you assume that the person was doing something bad in making the comment, or that they left it anonymously because because of some character defect.
–Jen