Are we talking about the US specifically? We have a Constitution and 200 years of legal precedent to protect our rights.
1) The fourth amendment and legal precedent make it clear that this requires a warrant obtained based on a standard of probable cause. The rights of a citizen to privacy is well protected.
2) I believe it is legal for the police to do this.
3) It is deeply troubling for the government to spy on religious groups. I know there are protections in policy on this (the FBI has has strict policies to regulate its use of undercover agents in churches mosques or synagogues)
I also know there are cases where the US government spied on churches. This included during the time of slavery where agents joined religious groups to find runaway slaves. And, during the civil Rights movement of Dr. King.
Most of us feel these were gross violations of the rights of Americans.
Of course, if there is probable cause and a properly obtained warrant it is a different matter.