The issue isn't as bad as initially feared, when the satellites hadn't finished orienting their solar panels and were thus extra bright (you can see a video of this below). The vehicles are only intended to last five years in orbit before descending to a fiery death in the atmosphere, for that matter, so this may only be a temporary issue. Elon Musk has maintained that the Starlink constellation "won't be seen by anyone" unless they're going out of their way to look.
Still, the executive was aware of the potential pitfalls and vowed to do something about it. SpaceX would ensure that Starlink "had no material effect" on astronomy, Musk said, adding that he'd asked the team to reduce the albedo (reflectivity) of the satellites going forward. He was even receptive to the idea of mounting telescopes on Starlink bodies to provide a clearer view of space. While these moves won't completely ease the minds of sky watchers, the company is at least aware of its potential impact in an era where a crowded orbit and space debris are very real issues.