Who has the right not to pay military duty?

Only servicemen who take direct part in hostilities and have received an extract confirming the payment of additional remuneration are exempted from paying the military tax.

https://www.kmu.gov.ua/npas/pro-vnesennia-zmin-do-postanovy-kabinetu-ministriv-a244 - Resolution of the CMU "On Amending the Resolution of the Cabinet of Ministers of Ukraine of December 30, 2015 No. 1161"