You could send an email/tweet to SpaceX and ask to be part of the Starlink beta program. They'd have to be granted a license for your country first, however.
Why - I suppose that government want to get tactical advantage over protesters by limiting information flow and making protest coordination more difficult.
How - both deep packet inspection + filtering and primitive solution - making communication services (mobile and broadband) stop functioning. Such things happen already in the past in Turkey, Egipt, Iran.
Depending on the type of filtering you could try to tunnel data across UDP (DNS?) or ICMP packets or configure hosts on both ends to ignore TCP RESET packets.
You could send an email/tweet to SpaceX and ask to be part of the Starlink beta program. They'd have to be granted a license for your country first, however.