I think it's very easy to go from "person has made claim which, if it actually became policy and was followed through harshly, would make my life very bad" to "that inimical policy is right here and much be opposed with all available force". It can be worth checking on the actual threat level.

A useful tool when you try to leave a defensive "I believe that..." stance is to leave it in a specific direction: The aggressive "I want to find out if..." stance. Because the anger means it is a strongly motivated behavior, and you can't simply stop being motivated - but sometimes you can build up an alternative motivation that happens to compete with the one you want to let go of, and pursue it. Of course this only works if you actually "want to know if" more than you want to defend "your" position - but since you're on LW, there's a good chance your thirst for knowledge is way above average, so maybe it can win out. I don't know if the following is true for you specifically, but for some people, issues like you're having can be the result of having had past confrontations about specific topics that went bad. More to the point, confrontations with people who were not open to sober evaluations and a search for common ground. In such situations, getting angry can be adaptive in that it at least gets you out of an unwinnable argument, so maybe you learned that behavior in that kind of situation. Does that ring a bell? If it does, simply recognizing that's what's happening is much of the work needed to change it. The rest could be to very consciously remind yourself who you're talking to, who you're not talking to, and be aware of the differences between them.