In conversational English, the sentence above is fine. However, for an ESL exam, I would use "had spread" (the past perfect tense).
Past Perfect tense is used when you have 2 actions in the past. The 1st action (chronologically) gets the Past Perfect tense, the 2nd action (chronologically) gets the simple Past tense. What matters is when the actions took place, not where in the sentence they appear.
So, in this example, the rumor was spread 1st, then respect was gained. So, "had spread" would be best for the purpose of an ESL test. Here's another example that could help you:
"Before I went to the meeting, I had prepared the report."