Health Care Equality and Modernization Act of 2022 This bill repeals the requirement for large employers to offer affordable coverage to full time employees and makes other changes to the health insurance system. Specifically, health insurance is no longer required to cover preventive care at no cost or include the essential health benefits. Individuals enrolling in health insurance who have not maintained continuous coverage over the previous 12 months are charged an extra 20% on premiums for each consecutive year without coverage, unless the individual is subject to similar state incentives to maintain coverage. States may enroll uninsured residents in high deductible health plans. Individuals must be permitted to opt-out of this coverage. The Department of Health and Human Services (HHS) must develop a risk adjustment mechanism for health insurance in the individual market. For residents of a state to qualify for premium subsidies or the health insurance tax credit in this bill, the state must permit health insurance with an annual limit on benefits to be sold on its exchange. The bill establishes an advanceable, refundable health insurance tax credit for taxpayers enrolled in coverage that does not cover abortion except in certain circumstances. States may (1) apply to HHS to use unclaimed health insurance tax credits for indigent health care; and (2) enroll Medicaid-eligible individuals in health insurance that qualifies for the tax credit instead of in Medicaid, at the individual's option. The bill establishes Roth HSAs (health savings accounts) for paying certain medical expenses and health insurance premiums. The bill eliminates the tax deduction for medical expenses. Finally, the bill also changes federal Medicaid payments into block grants.