Make sure you jet the stove for propane, otherwise it will push too much fuel. Natural gas is used at a lower pressure than propane.

As long as you use an appropriate regulator and hoses, fittings and thread sealant I don't really see any reason it wouldn't be safe.

Link to an adapter that sounds like what you want. If there's an actual HVAC or pipe fitter in here maybe they can verify but I think brass with gas rated thread sealant is best.

Anderson Metals 56120-0806 Brass Pipe Fitting, Adapter, 3/8" Male Pipe x 1/2" Female Pipe https://www.amazon.com/dp/B000BOAERY/ref=cm_sw_r_apan_glt_fabc_WB2NARQ43D4AEM7CYMHD?_encoding=UTF8&psc=1