Both Iglesia (Spanish for “church”) and Ecclesiastical (also similar English words: think of the book of the Old Testament, Ecclesiastes) come from the same root: the Latin Ecclesĭa for “church”, which comes from the Greek ekkalein (“to call out”). After all, a preacher does call out to God. That is his vocation, what he professes!
This pattern is not obvious because both the Spanish i‑g-l‑s maps to the English e‑c-l‑s. The I/E vowel shift isn’t particularly common while the g/c vowel shift is more common, but sometimes harder to recognize.