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It still amazes me that one, the mirrors are sensitive enough to the deformation of Earth's gravity to have an effect and two, that we are now very good at compensating for this now.I make telescope mirrors.
This problem was well understood since the time of Herschel. We just have better solutions now.
The fact that this is a space scope is irrelevant to the fact that gravity will cause issues. For any telescope, you have to account for differences in the way the mirror is deformed in manufacturing vs in actual usage, and the ways the deformation will change in usage as the scope is leaning at different angles. That is always a thing.
What is particular to the Hubble is that the load in usage is zero (which is unusual), so you have to think about it that way in manufacture. But deformations in manufacture are always an issue you have to account for somehow.
Look at it this way: there is an ideal shape that the mirror needs to have, usually a revolution surface of some conic section (parabola, hyperbola, ellipse, circle). The performance of the mirror will track the difference between the ideal surface and the actual mirror. The error allowance depends on the wavelength λ of the observed radiation.
Telescopes where the error is greater than λ/4 just suck, and are unusable. Good performance begins around λ/8. A great mirror may do better than λ/20.
For visible light, λ/4 is 100 nm, or 0.1 microns. That's 10 thousand times less than 1 mm. On that scale, the mirror is made of jelly. If you put it on a rough surface, it will deform. If you put your thumb on it, hold it for a minute so it heats up from your skin, then pull away, there will be a "mountain" left behind on the mirror, under your thumb, until it cools off again.
In many cases, the support structures for large mirrors are complex mechanisms that ensure the force is uniformly distributed across a large number of points on the back of the mirror. Even amateur telescopes built using the Dobsonian template use passive self-balancing support with 3, 6, 9, 18, or even more points, depending on the size / thickness ratio.