An interpretation can be meaningful/meaningless in two senses:
1. An interpretation can be meaningful specifically to that individual. There are no right and wrong answers in this case, and the number of interpretations is almost unlimited. If a person interprets Bambi as an allegory of the Civil War and they find this intepretation meaningful, then that interpretation is meaningful—at least to that person.
2. An interpretation can be meaningful in relation to the film. A reasonable person would agree that the film supports this interpretation. Several different interpretations can exist, but the number of meaningful interpretations, in this sense, is a lot more limited.
Many people may care more about their interpretations that fall under #1, more than #2. For these people, #2 is “meaningless” to them. That’s perfectly fine.
But I, personally, care about #2 interpretations, and when I talk about “valid/invalid,” “right/wrong” interpetations, I’m referring to #2.
Now let me say something else that I think is important: sometimes there is overlap between #1 and #2—sometimes they are one and the same thing. However, that is not always the case. Sometimes #1 is so far out-of-bounds that most reasonable people would say it isn’t valid. Now, to the individual interpreting the film, this may not matter. After all, it means something to him/her. But that type of interpretation, generally speaking, isn’t useful to other people and it doesn’t help us understand the film.
I agree that our interests, experiences, knowledge, memories, etc. influence the way we perceive a film—and hearing opinions from different people can be rewarding and meaningful. But you don’t think that these personal interests, experiences, knowledge, etc. can distort our judgment and opinions of films—that they clouding our perception and understanding of a film—as much as it can reveal hidden facets. I’ve seen this happen many times, with myself and other people. Our interests, experiences, etc., imo, often have to be mitigated; we should be aware of the way they’re affecting our judgments and opinions—because the effects are not always positive (at least if we want to understand the film).
As for your notion of refinement, I’m interested in hearing more about this, because it actually doesn’t sound too different from my own method. You seem to be saying that refinement balances understanding of great art (which would be intersubjective—involving critieria) and one’s personal experience with art.