We routinely push vehicles into intersections (not with contact) to make our way through. It is a generally accepted, as the option is I'm going to stand on the Federal Q2 siren and the Glover air horns until you move. I feel bad sometimes, but most folks who don't want to move seem to be lost and unsure of what to do. Most intersections we have to go into oncoming traffic to get through. When we do, at least the traffic coming at us has no excuse for not seeing us.
Either way, we're coming through, and a 40,000 lb fire truck tends to win when push comes to shove, and yes, we've hit/been hit plenty of times. I've had to write a few "Dear Chief" letters.
At one fire station I worked at it was a regular thing. After writing three letters in a year for my drivers being involved with vehicle incursions, I moved on.
As to us stopping, Maine law says we need to operate in due regard. If we're going to a minor call, we're slowing/stopping. If we're responding to a potential life-threatening call, we will push through a little faster, but still with extreme caution.
It is amzaing how many people pull out in front of us. It's a daily thing, I don't know what they think they are gaining, but I sometimes think it's a power thing. They seem to feel that we are forceing them to yield and they pull in front of us to make a point

. Doesn't matter to me, as long as we get there safe.