I think it would be good if we can convince these people that they are wrong. I know that an obvious way to do it would be an education, which will help A LOT. But as for now, do you think there are other ways to change these people's opinions?
Like would it be good if we could create a system that somehow will make the life of criminals who use Bitcoin harder?
I'm not really sure how you say bitcoin's reputation is bad because it's used in some cases illegal. Bitcoin allows anyone you use it, spend it for any purpose regardless of how you maintain privacy. Bitcoin is a decentralized currency that is basically not controlled by anyone including the government, so if you expect filtering for certain number of users, that means bitcoin is centralized.
Regardless you agree or not, money can always be misused by some people regardless of their reputation. Adoption is expected, but adoption acceleration is very low relation to the reputation of the bitcoin you are mean talking about.