A word that means "earn" without the "money" connotation?
There are a few substitutes I can think of:


信任是要靠努力得来的 (trust is obtained through hard work)
信任是要争取的 (trust must be fought for)
信任是要赢得的 (trust must be won)
信任是要经营的 (trust needs to be maintained)
信任是要用时间去积累的 (trust is acquired over a period of time)


If you are looking for a word, I think 争取[zhēngqǔ] is a good replacement for 赚 because it means to put in effort to achieve a goal and has no monetary connotation in it:


  争夺；力求获得; 力求实现