EDIT 1: https://media.defense.gov/2022/Jan/25/2002927101/-1/-1/0/CSA...
Seems like the NSA recommends a vpn to obscure VSAT use. They don't have much else to say about anonymity.
EDIT 2: Found this thread:
https://old.reddit.com/r/SpaceXLounge/comments/t5y67a/updati...
EDIT 3:
After some thought, I think Starlink will be robust against tracking. They should be harder to locate then VSATs which the author mentions in the Twitter thread. In comparison:
1. They are beaming to a constantly moving swarms of satellites rather then a geostationary satellite: a. So timing attacks can't be used to find a search path. b. The beam is moving to even he a plane pickup on a signal it would quickly lose it as the beam moved. Although there is a workaround I won't mention.
2. They are lower powered so the signal is weaker. I assume they are just as directional.
3. They are smaller and harder to spot.
4. They are much more numerous.
5. They are portable.