Safe Connections Act of 2021 This bill establishes requirements for protecting and expanding access to communication services for survivors of domestic violence, human trafficking, and related harms. At a survivor's request, a mobile service provider must separate from a shared mobile service contract the survivor's line (and the line of any individual in the survivor's care) from the abuser's line. A survivor requesting this must verify through appropriate documentation that an individual under the shared contract committed certain criminal acts (e.g., an act of domestic violence or trafficking) against the survivor. A provider may not charge fees or impose other requirements on such requests. Additionally, a provider must separate the line within 48 hours of receiving a request, allow requests to be made remotely, treat information in requests as confidential and dispose of it within 90 days of receipt, and make information about the options and process for requests available through consumer-facing communications (e.g., websites). The bill (1) provides liability protection for a provider's act or omission related to compliance with a line separation request, and (2) requires the Federal Communications Commission (FCC) to adopt rules for line separation requests. In addition, the FCC must adopt rules requiring communication service providers to omit from consumer-facing logs any calls and texts to domestic violence and similar hotlines while retaining internal records. The FCC must also (1) temporarily allow survivors to participate in the Lifeline program (which subsidizes telephone and internet service for low-income individuals) regardless of whether the survivor otherwise meets eligibility criteria, and (2) evaluate expanded access to the program for survivors.