Can I reasonably ask for an exception to be made? How should I state
You can always ask.
Just indicate that you would like a transfer. Talk about the value you would provide in the new role.
By all means don't bring up that you "feel blindsided by this change" in policy. That would be silly. You must know that it wasn't changed solely to negatively impact you.
When I ask my manager to approve my internal transfer request, is
there a risk that I will be fired from my current role?
I suppose there's always a risk. But it would be shocking if you were fired over it.
There may be a bit of blowback from your current manager regarding your desire to leave their team so soon. You have to anticipate this. Often the best ways to counter that feeling is to emphasize how much more value you would bring to the company in the new role than you currently do in your existing role.
In the professional world, do managers think that a "internal transfer
request" is a sign that the employee is about to jump ship, and would
rather fire him first?
In my experience, it's less about "jumping ship" to go to another company. It's more about having invested time and money in training you for your current role, only to see you leaving for another department very quickly.
The worry would be that after another 6 months in the new role you would be bored again and would want yet another transfer.
Companies want to keep employees around and would prefer to see you transfer internally rather than leave the company. Still, they want you to contribute in the role you hold.
It takes time to get a new employee onboarded and up to speed in a new role. In my experience, many new employees may just be hitting their stride at the 6 month mark. That's why companies have a minimum time limit on internal transfers. I haven't yet worked for a company that had a limit less than 1 year.
If you request a quick transfer once, I wouldn't worry much about being fired. But I wouldn't make a habit of transferring as soon as possible. That tends to be a bad look.