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While a complete answer on this subject would take volumes, there are many Christians who were martyred, not for simply being of the wrong religion, but for actions they felt compelled to take because they were Christians. In the Roman era, Christians weren't persecuted because they had a different religion. There were lots of different religions in ancient Rome. However, Christians refused on religious grounds to participate in sacrifices to the good health of the Emperor. So in addition to being superstitious, athiestic, sex-cultists, the Christians were also anti-Roman.
If you carry that forward through time you see a pattern of martyrs being condemned not just for religious differences but also for causing some other type of offense. These offenses have been real and perceived, political and personal. I personally find the cases of daughters murdered by their families for disobedience, usually refusing to marry, to be the most horrific.
The 10 20th Century martyrs depicted at Westminster Abbey include:
Dietrich Bonhoeffer who was executed for subverting German law and conspiring to assassinate Hitler
Martin Luther King, Jr assassinated for his involvement in the American Civil
Rights movement
These martyrs like so many others were not persecuted because they were Christians but because of what they did in the name of Christ. Even more recent cases of Christian persecution, especially in the Middle East, have more to do with real or perceived political affiliations and less to do with actual religious differences.