In my view there is such a perspective: quantum mechanics. So far as we know its predictions are valid for all observers.

But what that means is that we have to readjust our classical conceptions about what a "property of a system" is.

The word "property" in general is just a logical concept, and doesn't carry any intrinsic ontological implications. There can be mathematical properties, physical properties, properties of thoughts and dreams etc., and this way of talking about things doesn't by itself imply any specific ontological interpretation. It's just a feature of the structure of language.

About physical properties specifically, if we derive our concept of physical property from quantum mechanics, instead of trying to retain the inadequate classical meaning, then physical properties are exactly those represented by the state vector: e.g. its projections on to each of the basis vectors corresponding to some observable.

True, as is well-known from the Bell and Kochen-Specker theorems, we can't consistently say that a quantum state has some specific value of its observables independently of interactions with other systems, but this is just the classical conception of a physical property (formalized, e.g., by a real-valued function on phase space).

But quantum mechanics doesn't thereby force us to say that a physical system has no definite properties. Instead, we can reconfigure our conception of physical property to make it compatible with quantum mechanics.

Then in general the properties of quantum states are probabilistic (at least some of them - the dimension of its state space, for example, is not), but the theory unambiguously assigns to a state the probabilities that the various possible measurement outcomes will be observed. These probabilities are among that state's properties, and all indications are that these probabilities are objective features of the state, independently of our ways of representing the state.

In fact the dependence goes in the other direction: this (objectively) probabilistic character of quantum states (among other things, like the quantization of energy exchanges) is what forced us to change the way we think of physical states.

if your definition requires universal observer agreement you already have that issue with special relativity / light cones / the spacetime metric.

many worlds posits a single universal quantum state it's just only partially accessible to observers, which is different from saying that it simply doesn't objectively exist.

maybe it depends on your definition of objective

No objective reality or no single universal frame?

Reproducable reality from x frame seems non-arbitrary if not objective.

That phenomenon was known in classical physics since 500 BCE: https://en.wikipedia.org/wiki/Blind_men_and_an_elephant