The above poster are talking about special relativity only. It's "special" because it's only specific to inertia frame. So for the sake of completeness I will talk about general relativity, which follows the principle of general covariance, in which all frame of references are valid; in other word, all time and distance measurement are relative. This should show you the real crux of the problem: it's not that "acceleration is absolute and speed is relative", but rather "physical constants are differed between accelerating frame".

To achieve general covariance, general relativity comes with metric tensor. The metric tensor measure proper time and proper length, and this way we unshackle the concept of length and time from the coordinate. The metric tensor is obviously needed since an arbitrary coordinate system means you can pick system in which directions are distorted (e.g. 2 units to the right has equal length as 10 units to the front).

So you're now free to rotate your coordinate system at will. These distance galaxy will move at insane speed in your system of coordinate, but if you look at the metric their speed is completely normal.

So what's the lesson from this? Coordinate system is a completely arbitrary construct that has nothing to do with actual physic. There is nothing wrong with an object moving fast according to the coordinate system. If you have a rotating coordinate system, it's as strange as having a scaling coordinate system where the length of the axes changes over time; in either case, far away objects will appear to move too fast according to the coordinate system, but nothing actually physically change.