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Yes, nature is not objective - it is relative. Mathematics is a discipline that is based around an objective framework. Lines and planes are mathematical constructs. Mathematics gives us an objective framework that can be used to model a natural world, but they are just models.
Some things are "line-like" or "plane-like," in that modeling them as lines or planes is helpful to describe them. You can measure a distance "as the bird flies" because birds fly in lines compared to how humans travel along roads and paths. You can describe a dense, heavy, falling object as traveling in a straight line, because air resistance may be negligible over short distances.
A model is only useful insofar as it accurately represents reality. Lines and planes are mathematical constructs, and they may be incorporated into models that describe real things. "A beam of light crossing a room travels in a straight line" is probably a useful construct because the effects of gravity and refraction of the air are probably negligible for nearly all purposes. "The surface of a pond is a plane" is probably an acceptable model for a cartographer, since the height of ripples and the curvature of the earth are negligible at that scale.
The initial question was not "Do straight lines and flat planes model anything in nature," but whether they exist in nature. They do not. They only exist in mathematics.
The curved light path is because a mathematical transform is done between two different frames of reference.
It's no different than taking a mathematically straight line and performing a transform function to map it to a curved coordinate system. Because you allow transformation functions, there would also be no straight lines in math.
Light travels along geodesics that curve because spacetime itself is curved. Geodesics are curves that minimize distance between two points in a curved space. They are considered straight lines in a curved space, but it's right there in the definition. Geodesics are curves. Our reality is a curved space, therefore straight lines in our curved space are curves. They are not straight.
Our reality is not matiematically flat. It is matiematically curved.
From the point of view of light, it is traveling in a straight line. It does not observe the curve therefore spacetime isn't curved to it. There is no preferred reference frame.
It is the same with special relativity. If a particle is moving at near light speed, you observe it as heavier. But from the particle's point of view it is you who are moving and you are heavier.
Curved spacetime is a mathematical transformation to reconcile the different reference frames in the same way time dilation is a transform between reference frames.
There is no absolute frame of reference.
You're not taking about the same thing as everyone else.
You're comparing reality to reality, curvature to curvature. We're talking mathematical theory. There's nothing about our reality of spacetime that meets the definition of mathematically flat.
Type however many paragraphs you want about reference frames. None of them adhere to being mathematically flat. They are all curved spacetime.
There is no absolute frame of reference!
Light travels mathematically straight in one frame of reference but curved in another. Both are correct. You use mathematical transforms to map one coordinate system onto another in the same way you can map a mathematical straight line into curved geometry.
https://www.einstein-online.info/en/spotlight/equivalence_light/
Look at the example they gave of light in an accelerating elevator (which is actually an example written by Einstein in one of his books on relativity). One has straight light and the other is curved. Both reference frames are correct.
There's no absolute frame refrence in physics. We're talking math theory here.
Light in an accelerating elevator is physics. Light in an anything is physics.
https://xkcd.com/435/
The math that describes light in one reference frame is a mathematically perfect straight line. In a different reference frame the math that describes light is curved.
Just like a straight line in one coordinate system can be transformed into a curved line in another system.
You're just repeating yourself. It doesn't make you right.
A straight line in a curved space that adheres to the curved space is still a curved line. An actual straight line exists between the two same points that is shorter than the path light would take. That is the mathematical minimum distance.