2) is correct as impose is a transitive verb and takes an object, in this case "your opinion". 1) is incorrect as intrude is intransitive and does not take an object. It is correct to say, "You must not intrude," or, "You must not intrude on others," but to "intrude opinions on others" is incorrect.

Hi Nanako, These two phrasal verbs are quite synonymous but there is a slight difference, and to intrude one's opinions isn't appropriate. To intrude means interfering, so for example, asking too many questions to someone: this can become intruding. To 'impose' is more than that: the person is now "forcing" the person to follow. Bob imposes his opinion on Mary by 'forcing' her to follow and accept his opinion ONLY. So here, Bob would tell Mary to think that ONLY Manchester is best and nothing else. In summary, they are synonymous but to impose one's idea is stronger than just intruding. Also you cannot really say 'to intrude my opinion on someone else'. Hope it helps Feel free to drop me a message if you want more help! Charlotte