I forgot to answer this.
I think at the extreme end it could be difficult to conceptualise something that’s so different from what we call life and yet is still a lifeform. At the minimal end, though… what is life? (baby don’t hurt me) Is a virus alive? One definition would say no, because it can’t replicate itself without a host. But why does that have to be the definition? And if the definition is the ability to self-replicate, you can design some extremely minimal chemical systems that can self-replicate, so are those more like life than a virus? I have no idea.
The carbon thing I’m actually more or less onboard with. I don’t think it’s anthropocentric logic so much as it’s chemical reality; the periodic table is what the universe has to work with and there aren’t very many options for elements that can form complex molecules. We’re carbon based not just because of relative abundance of C, H, N, O, P, S etc but because those are the elements that are capable of forming different bonds and hence the kind of structures that can form templates of themselves for replication.
The old classic was “hey what about silicon-based life, that’s just one down the periodic table from carbon”, but silicon atoms are just too big to form multiple bonds in the way that carbon does. I wonder if anyone’s thought about life based on the kind of complex shapes that silicon/aluminium/oxygen complexes form - big cage structures and stuff.
The other chemical limitation is the water thing -why do we look for planets that can have liquid water? It comes back to the idea that anything we would recognise as life would involve self-replicating chemicals. That means liquid-phase chemistry, almost certainly. It also probably means catalysis. The list of possible substances that meets those requirements is really small - water and ammonia are the most likely for boring chemical reasons. Liquid hydrocarbons like on some moons of Saturn/Jupiter are possible but maybe less likely because they don’t have the same kind of chemistry as water and ammonia.
But I do think you’re absolutely right that we need to be really careful to avoid anthropocentric logic with these things. It’s kind of the same as viewing history through a European viewpoint, but massively magnified.