MOSCOW—Residents of the Russian cash emerged Tuesday from a rigid coronavirus lockdown, a working day right after Moscow authorities declared they would carry important restrictions in a transfer Kremlin critics say is meant to undertaking safety and normalcy ahead of two important events—even as infections in the metropolis continue to be substantial.

Muscovites, who had been purchased to continue to be at home for far more than 10 months, can now go outside devoid of limitation, visit hair salons and take component in selected other activities—the beginning of what officials say will be a phased…