This is a cop-out. It might make for a good episode (or a bad one) of Star Trek, but in the real world, life's going to be made out of particles. Likely even out of atoms/molecules.
It will be recognizable, in that it is self-sustaining... it creates itself. It will, for lack of a better term, "do things".
The chemistry might be weird (hell, we almost expect that). The effects might be subtle (at minimum, we imagine we'll need microscopes, but it gets more difficult from there).
But none of these things are incomprehensible. "Incomprehensible" is probably nearly non-overlapping with "life", if not outright incompatible.
> But should we find green plants on another planet, can we instinctively conclude that they indicate life as we know it? Probably not, as such assumptions hinge on our Earth-centric model of life.
This is incoherent. I don't even know how to parse it.
"We found photosynthetic organisms on another planet, but are they life?"
Like, seriously? Are you saying that plants aren't really alive here on Earth, or that plants are only alive if on Earth? If I take a potted plant to Mars, "is it really life as we know it"?
> We may have to accept that some entities might exist beyond our grasp of understanding and should develop novel tools that seek not only life as we know it,
I think that some people learn to think like this because their mouth-breathing public school system teachers gave them B+s for this bullshit in 7th grade. It's bizarrely bad. Have you never listened to yourself?
> Such a perspective fundamentally changes the narrative of our search for alien life.
Yes. It hobbles the search in any number of ways. Entire generations of children grow up thinking this poorly. Influencers and politicians start thinking such is somehow clever or insightful, and money/effort is wasted on it.