I don't see why they would. The stars typically used for astronavigation are very bright; brighter than starlink satellites. A brief web search leads me to believe typical starlink satellites have a magnitude of around 5 or more, while the stars typically used for astronavigation have magnitudes of less than three (https://en.wikipedia.org/wiki/List_of_stars_for_navigation)

Even if that weren't the case, it's easy for the human eye to distinguish a star from a LEO satellite; the satellite is the one that's moving fast. I see no reason the sailors couldn't simply ignore the satellites.

Starlink Satellites are only visible for short periods just after sunset and before sunrise, because most of the night they are in the earths shadow.