1. Especially in democracies (and especially the US, which is a federation in which the “reserved powers” belong to the states) there will be debate over whether specific law is valid. American law is much more complex than most, since it it debateable if public health measures are the responsibility of the states or the federal government, and how the protections of the First Amendment of the Federal Constitution (and the state equivalents) apply.
2. If the Rabbanim of the city mandate a lockdown, even if it would be held unconstitutional if done by the government, a strong argument can be made that our law (rather the Dina Malchusa Dina) applies, even if the Rabbanim have been poorly advised.
3. Whether the policies banning religious services but allowing similar events (with many people gathering together, such as left wing political ralles) is constitutional is very much debateable. In the past we often had to decide how to deal with anti-Jewish laws (e.g. close the synagogues) but have rarely needed to worry about general laws directed against all religion (e.g. close down all houses of worship). A similar situation did arise when militantly atheistic socialists took over Russia about 100 years ago, and passed laws against all religions (not just Jews), and I believe most rabbanim held that Dina Malchusa Dina did not apply, and we honor those who refused to obey these laws.