The short answer is YES, moving expense payments are taxable income.
For the 2018 thru 2025 tax (calendar) years, moving expenses covered by the employer are taxable income for the employee. This is a change introduced through the Tax Cuts and Jobs Act of 2017. In other words, as far the IRS is concerned, moving expense payments look just like salary. The employee whose moving expenses have been covered by the congregation, either through direct payment or reimbursement, will owe income taxes on the amount. And, as with salary, Social Security/Medicare taxes also must be paid: ministers pay the full 15.3% (SECA), while for non-ministerial staff the cost is split between employer and employee (FICA). Congregations are encouraged to gross up their reimbursement to include the amount of estimated taxes.