Yes, FHA allows cash out refinancing.
A Cash-Out Refinance is a refinance of any mortgage or a withdrawal of equity where no mortgage currently exists, in which the mortgage proceeds are not limited to specific purposes.
For additional information see:
Handbook 4000.1 II.A.8.d.i.(B)(1); II.A.8.d.ii.(B)-(C); II.A.8.d.v available at https://www.hud.gov/program_offices/administration/hudclips/handbooks/hsgh
Mortgagee Letter 2019-11 available at: https://www.hud.gov/program_offices/administration/hudclips/letters/mortgagee