뼈가 굵어갔다 => matured in character and disposition gradually / grew from accumulated experience.
민주주의와 기독교 신앙으로 뼈가 굵어갔다. => (I/we/they) matured steeped in democracy and Christian faith.
뼈가 굵어갔다 is an idiomatic expression which literally means "the bones got thicker[hardened]".
It means gaining experience and maturing over time to come into one's own.
뼈가 굵었다 and 잔 뼈가 굵었다 (The fine bones got hardened) are also widely used.