This book specifies the difference as:
martyr for something: smb. who is made to suffer severely for a cause
martyr to something: smb. who is acutely inflicted by something
Oxford dictionary also tells us this:
(martyr to) a constant sufferer from (an ailment):
Other online dictionaries don't seem to explicitly specify a difference, though all example sentences for "martyr to" contain an ailment.
Yet, I've seen the usage "He/She is a martyr to his/her cause/country" a lot. In fact, google gives more hits to the "to" use than the "for" use.
martyr to his cause: 315,000 uses vs. martyr for his cause: 285,000 uses
martyr to his country: 371,000 vs. martyr for his country: 266,000 uses
So is there still a difference between the two in modern/current use? Is this a case of colloquial use being inconsistent with grammatically correct use? Is this a US vs UK issue? Help, please? Surprisingly google is not yielding even a single article discussing this usage.
ETA: Ngram comparisons that have now only increased my confusion. It seems "martyr to cause" is significantly more common is usage than "martyr for cause".
Diagrams for Cause and Country
Best Answer
There are actually two different meanings and usages of "martyr to".
Being a "martyr for his cause" (or country) is well-understood. It means the person sacrificed themselves for the cause. Being a "martyr to" something generally means that you suffer as a result of something: a "martyr to back pain" means that you suffer extremely from back pain.
The other use of "martyr to", means that his cause (or country) treats him as a martyr. For example "Joan of Arc is a martyr to the French", means the French consider her a martyr. The English, on the other hand, don't, so she is not a martyr to the English. Another example might be "Martin Luther King was a martyr to the American Civil Rights movement". Civil rights proponents considered him a martyr, other people didn't.
The many occurences of "martyr to his cause" and "martyr to his country" are most likely to be usages like that.