Just lie and say it’s for religious reasons.
There’s nothing immoral about lying to tyrants…
Actually, on my religious exemption form I told them that I had religious, scientific, and political reasons for not taking it, and that I didn’t need to explain myself any further. I got the exemption.
The religious exemption is illusory. It is like a unicorn. It exists on paper but does not exist in reality.
See too, "government of the people, by the people, and for the people." That perished.