Why do members of the Mizrachi movement wear colored shirts, sandals and not wear hats and jackets? Where is Kavod Hatorah, respect for yourselves, and isn’t Al Pi Halacha one obligated to dress as if he is going in front of a king?

The Shulchan Aruch (Orach Chayim 91) requires dress for prayer which would not cause embarrassment in the presence of important people. For instance, one should wear socks if this is local custom. In many communities, the clothing you mentioned is commonly worn, even in the presence of important people. Suits and hats create a dress code that distinguishes the orthodox Jew in a way that creates a real social barrier. Many people see this as desirable, others do not, but it is not a halachic requirement.