ujm > That Chilonim don’t accept תורתו אומנותו as a valid exemption is absolutely no reason anyone shouldn’t utilize that exemption, regardless of Chilonim not accepting it.
Gemora brings such example in Bava Basra – Rabonim refused to pay roman tax. The “chilonim” did not like that. Rabbis told them – you can leave. At the end, after the last launderer left, the romans abolished the tax. So, just move to one town, let Tzahal leave you alone. That is fair. Accepting protection and not paying for it is against halakha.