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.