I think the problem is that being killed for one’s faith is actually a fairly nebulous concept.
Take a simple case. You believe X. I kill you because I think that people ought not to believe X, and that those who do believe X deserve to die. I think most people would have no difficulty in concluding that you had been killed for your faith in X. But this is not, in fact, a very common scenario.
Suppose that, on account of your belief in proposition X, you undertake action Y. You consider that action Y is something that your beliefs require of you. I kill you because I belief that people ought not to undertake action Y, and that those who do undertake it deserve to die. I am utterly uninterested in your reason for undertaking action Y. Had you had an entirely different motivation, or had your action been motiveless and capricious, I would have killed you just the same.
Have you been killed for your faith? From your perspective, undoubtedly, yes. From my perspective, definitely not. From the perspective of a third party? Well, that depends.
Suppose Action Y was a refusal to offer sacrifice at the altar of the Emperor-God. Most people, I think, would accept that Christians who were persecuted in classical Rome for their refusal to participate in the civic religion were being persecuted for their faith.
But suppose Action Y is giving shelter to Jews who are fugitives from the Nazis in some part of occupied Europe. If you do this because you feel ethically bound to do so, given your beliefs, are you then persecuted for your beliefs? Or for breaking the law against giving shelter to fugitives?
Suppose your action is a refusal to serve in the armed forces, motivated by your ethical beliefs. If you are punished for that, are you being punished for your beliefs, or for failing in your legal civic duty to participate in your country’s defence?
What if your action is a refusal to pay taxes?
What if it’s a refusal to observe the laws regarding animal slaughter/processions in the street/not ringing bells at night/taking an oath/marrying only before a clergyman of the established church?
I cautiously suggest that we’re much more likely to recognise someone as being persecuted for their beliefs in this situation if they are beliefs that we share, or sympathise with. Thus the Christian who is killed for refusing to participate in the civic religion is a martyr for the faith, whereas the unreconstructed Mormon who marries six wives is prosecuted for his practice of bigamy, and not for his religious beliefs.