We are of like mind. (also we are of like mind on this topic, etc)
Our personalities are very alike.
On the other hand, we could point out that there are people that "have complementary or similar personalities"; take for example a case of a couple living under the same roof, they could have complementary traits and personalities.
But one seeing from outside would state that "opposites atracts" what wouldn´t be actually the case.
People of similar personalities tend to be friends, or constitute a clique, group who share the same interest or aim, etc. So, they are like-minded people.