Dogma itself isn't a problem. For example, the belief that the Constitution and the values it represents are the cornerstone of American society is a type of dogmatic belief. Dogma itself doesn't pose a problem unless dogma intertwines with fundamentalism, where the violation of dogmatic beliefs calls for unduly harsh punishment.
Dogma by definition is the acceptance of principles laid down by an authority as incontrovertibly true. This is a problem, you should only accept anything that you yourself have verified.
Dictionary.com lists four definitions:
1. an official system of principles or tenets concerning faith, morals, behavior, etc., as of a church.
2. a specific tenet or doctrine authoritatively laid down, as by a church
3. prescribed doctrine proclaimed as unquestionably true by a particular group
4. a settled or established opinion, belief, or principle: the classic dogma of objectivity in scientific observation.
Especially as in the case of the fourth definition, not every definition of dogma requires the negative aspects as you have presented them. The American belief in constitutional democracy and republicanism are both dogmatic, as is the notion of objectivity in scientific observation, as the definition points out. These are things society overwhelming accepts as good things, so the problem is not with dogma, it's fundamentalism. A global dogmatic belief that it is wrong to harm other individuals would be immensely beneficial to humanity, but there are religious fundamentalists to who believe harming others is justified by their religious dogmatic beliefs. The problem there isn't dogma, it's fundamentalism.
Which constitution? As far as I know it has been amended 27 times, the only constant is change. A shared belief that its a bad idea to harm others is not based on dogma, but rather self knowledge.
"Constitutional democracy" is the dogmatic belief, not the Constitution itself. The fact that we keep amending it to make it work for us instead of just chucking it out and declaring the idea a failure when it doesn't proves my point further. We are dogmatic in our adherence to constitutional democracy and republicanism. And a shared belief that its a bad idea to harm can come from self knowledge and be dogmatic. They're not mutually exclusive. That's kinda my whole point in saying dogma isn't the problem, fundamentalism is.