A skylink is not a passive receiver. It engages in a directed dialog with the satellite stream to uplink as well as down link. True, this is aimed to follow each satellite and steer electronically to the next - so emissions to the side are reduced - not not eliminated, as the radiation pattern is not a precise beam - the physics dictate a number of lower signal sidelobes. It is quite true that it works fine through a black/white/green trash bag but an enemy can find them.
Musk suggests use only when needed, for short intervals, perhaps at night if the data is not needed to deal with targets etc and other combat related reasons.
It is also possible to make a small solar powered 'chirper' - a small array a few inches across can be hidden in a tree far from you that would emit a spoofing signal crafted to be in the frequency band and have similar properties to the true ground signals. This would cost perhaps $5 or so. It would show up on detection apparatus much like a true Starlink and a few dozen deep in a forested area would make a fake signal. Operating on the principal that the enemy would need to check them out one by one, if they could be made in such a way that the signal had a close enough resemblance to a genuine Starlink. This would be coupled with the selective use-when-needed Starlink activations would make signal tracking a fools game and waste time. Fingerprints would need to be wiped, and a pair of small lithium cells and a solar array to make 8 volts or so should be able to power a low power Starlink spoofer that could be hung in a tree trunk facing the sun. The signals are low powered, so an hour of sun/day should be able to power a 50 Mw transmitter for a few weeks - a 50 mw signal in these bands is large and easily can spoof a Starlink signal. A small control board of low power GasFets should reach the frequencies needed. Design staff at Starlink HQ could craft such a spoofer in a day or so and it could be made with discrete parts on a small board, placed in a plastic baggie with the solar array outside.