Interestingly, your link has this:
(e) prosecution or punishment for refusal to perform military service in a conflict, where performing military service would include crimes or acts falling under regulation 7 [exclusion clauses, see more here]
And that reminds me of the ultra-orthodox in Israel.
Haredi conscription law sparks tensions ahead of protest | The Jerusalem Post (jpost.com)
So potentially the Heredi could claim asylum for refusing to serve. And I did say above that maybe armies should be made of secular/ atheist folk.
That create an interesting conundrum that I can't answer. I am all for asylum, so if they were to apply of course I would agree. But we have talked about religious extremists, and these folk fit that bill. And I would guess that they are a significant voting block in Israel who vote for the more hawkish politicians.
Religion sure makes things complicated.