(I'm not speaking for any of my current or past employers, just for myself, and how I've seen this play out. One employer being a telescope impacted by Starlink, and the other being SpaceX, I want both sides to succeed.)
First, astronomers know that satellites can disrupt observations. They've known for a while, and have had to deal with things like flares from Irridium satellites, which were probably when these problems were first taken seriously. (It was a design defect where shiny panels would reflect the sun in a very efficient way).
Astronomers use all sorts of image processing, because satellites aren't the only noise in the picture. The CCDs have to be kept cryogenically cool, and there's all sorts of electrical noise as well. There's not a lot of photons being collected in the grand scheme of things, so dealing with the noise floor is a real problem. There are all sorts of ways for removing tracks. And don't forget weather!
Now, that being said, even I was confused why this would cause a problem. The satellites are in low earth orbit, so low that they won't be able to reflect the sunlight, since they are in earth's shadow. Only during twilight and dawn will satellites be in the right position to reflect the sunlight back to the ground off of some panel.
Now, these are not prime observing hours for many people, since it is still not as dark as it could be. So most people point into the darkest parts of the sky (up) rather than at parts where there is still twilight (like nearer the horizon).
But for some types of observations, like near earth asteroids, you want to point into the evening sky to look for them, since that is one of the places you want to look, and the sky conditions should be good enough. In these pictures you'll get streaks of light as the satellites pass through.
Even if there is no light reflecting, these satellites could occlude a distant star or galaxy momentarily. You wouldn't see a streak as much as the light would go away and come back. This would affect how bright you see the star, since over the time of the exposure (let's say 30 seconds) you'll collect less light while something is blocking the light. This can also make it a bit more tricky to look at variable stars, where the light gets stronger and dimmer naturally.
I would say that astronomers definitely knew about these problems, since they have to deal with all sorts of similar problems, but the pitch didn't get fevered until people saw the first set of Starlink satellites and just how bright they were. SpaceX moves a lot faster than astronomy.
As for SpaceX not thinking about the astronomical implications of Starlink, I could believe that. I think most of them were more concerned with if it is possible rather than the implications of doing it. As much as I would think the two fields would know more about each other, I find they are very different and run in different circles it seems (launch vehicle industry vs astronomers), so I could easily see not much cross pollination between the two. For example, there were lots of NASA astronauts and air force people visiting SpaceX, but I don't remember one astronomer (not that I met everyone).