Do missionaries destroy the host country's culture?

I think good missionary will not destroy the culture of the people that they share Jesus with. If you read the Bible Jesus and His disciples shared salvation to many many cultures . They taught each new believer to respect each other and not look down on them , and not expect them to be all the same. I think the big problem is that Westerner's go in and mix traditions up with the gospel and expect the people to conform to these traditons . For example dressing up , using a certain Bible, having the service at 11am , when in some places that may be an aweful time to have church . There are many examples but I can't think of the all right now.

If it can be said that missionaries destroy the host country's culture? Then it should follow that Islam destroys the host country's culture when they come in and dictate to that countries citizens convert or die.

Yes, culture is already rooted in our personality. New set of beliefs will only change people who adopts it. Even though you adopt new beliefs there will still be part of you that belongs makes us identified with this culture or values.