tldr; some modelling has been done with a lot more to do, but generally the impact of these constellations is fairly negative, but potentially manageable.
Ok, there's a lot to unpack here. First things first, while people have been aware of Starlink and have thought of it, modelling the impacts to observatories hasn't happened as of yet in quite a few places.
The main observatory which has had modelling done, LSST, released this statement;
LSST is particularly sensitive to bright trails of these satellites, due to LSST’s unprecedented product of field-of-view and light collecting area. Most LSST images will contain such a trail if plans for multiple LEOsat constellations materialize. The first group of Starlink satellites are sufficiently bright during dawn and dusk (when LSST would be surveying) that the trail would exceed sensor saturation, generating uncorrectable artifacts in the data
AURA (the owners of LSST) provided some additional information;
The LSST Project Science Team has been simulating the potential impacts to LSST observations. Their latest update of preliminary results from November 2019 indicates that (assuming the full deployment of planned satellites) nearly every exposure within two hours of sunset or sunrise would have a satellite streak. During summer months there could be a 40% impact on twilight observing time (less in winter) and saturation of sensors by the satellites can continue well past astronomical twilight. Because of scattered light in the optics by the bright satellites, the scientific usefulness of an entire exposure can sometimes be negated. Detection of near-Earth asteroids, normally surveyed for during twilight, would be particularly impacted. Dark energy surveys are also sensitive to the satellites because of streaks caused in the images. Avoiding saturation of streaks is vital. The LSST team notes that “For the full Starlink constellation, at any one time during the night over 200 Low Earth Orbit (LEO) satellites will be visible. This will increase by the mid-2020s with additional planned constellations of LEO satellites.”
I've found some other astronomy authorities that have released statements relating to the problem at hand, but they don't have that much information as to potential impacts of these constellations.
As of June 2019, the IAU stated that
We do not yet understand the impact of thousands of these visible satellites scattered across the night sky
In regards to this lack of information the AAS created this survey is to gather as much information as possible about the impacts to various observatories so that they can be better informed:
From what I can tell, the results of the survey aren't out yet and of course when released it will provide a lot of insight into the potential impacts and how to manage them.
These are the properties which the AAS expect of a constellation of 1,584 Starlink satellites.
- Consider satellites to be visible only when altitude ≥ 30 degrees and in direct
Sunlight or Earth's penumbra
- magnitude 5
- satellites cross sky in 4 minutes
- 6-9 satellites visible at any time during 1-hour starting (ending) at 12-degree -evening (morning) twilight
- spatial density on sky ~ 7E-4 deg-2
- angular speed across sky ~ 0.5 - 1 degree / sec
In regards to radio astronomy, the NRAO were happy enough with SpaceX Starlink, though there might be concerns with other constellations such as Oneweb.
In reference to the previous point, all of this comes with the caveat that Starlink is potentially only one of perhaps 4 or 5 LEO constellations. Even if SpaceX acts responsibly you still have to convince all of the others to do so as well, which might be difficult.
SpaceX and AAS are working together on ways of reducing the impact of Starlink to astronomy. AAS on mitigating Satellites Constellations impact