Preventing Election Subversion Act of 2021 This bill establishes certain federal criminal offenses related to voting and sets forth additional requirements for federal elections. The bill makes it a crime to (1) intimidate, threaten, coerce, or harass an election worker (i.e., an election official, a poll worker, or an election volunteer) with the intent to interfere with the official duties of, or retaliate against, the worker; or (2) publicly disclose restricted personal information about an election worker or an immediate family member with the intent to threaten or cause harm to the worker or the family member. In addition, the bill restricts the ability of a statewide election administrator to remove a local election administrator. A statewide election administrator may suspend, remove, or relieve the duties of a local election administrator only for inefficiency, neglect of duty, or malfeasance while in office. Further, the bill establishes certain requirements for challenging an individual's eligibility to register to vote or vote in federal elections. The bill also sets a minimum distance for poll observers.