But it's not applicable, because an "observer" in relativity is not a subject having perspectives, feelings, beliefs, etc. It is an abstract mathematical point

But it's not applicable, because an "observer" in relativity is not a subject having perspectives, feelings, beliefs, etc. It is an abstract mathematical point moving through space. "Reference frame" is really the proper term, not observer or subject. And the proper time that passes in a given reference frame is an objective fact in relativity, even though that measurement cannot be directly applied to other reference frames without transformation. "Objective" doesn't mean "experienced from all perspectives in the same way". Two different observers of a cube will get two different perspectives of the cube. The cube is still a single, objective, observer-independent reality. The same applies to relativistic time. It's a single reality (part of the spacetime manifold) that is measured differently in different reference frames. The different measurements must be consistent with one another according to a system of formulas. Just as different perspectives of a cube must be consistent with one another based on (1) the cube's objective existence in space and (2) the formulas of optics which determine the perspective each observer will receive. It may be helpful to think about a more mundane example. Google search results for a given search term depend on who searches, which makes them relative. But they don't depend on the feelings of the searcher and hence are not subjective.