My Cortina rack needs to have the tie rods shortened by about 30mm per
side.
Is it acceptable after shortening, to extend the thread on the tie
rod, or have the threads been rolled? If the threads have been rolled,
would threading with a die damage the grain structure in a
significant and potentially dangerous manner?

I presume the rack actually fits and you're not just shortening the most obvious parts?
Inspect the threads on the tie rods and if they've been cut, then it's fairly safe to asume they can be cut further. However, if they've been rolled, then you'll probably damage the die trying to extend the threads and even if you don't wreck the die, the resultant threads will probably be quite granular and flaky.
I wouldn't risk cutting them if the original threads have been rolled.

If you look at the threads you will see the dia of the thread is bigger than the tie bar dia --- so no way can you cut the threads using a die.
Even if you could shorten them as they come from the factory the stock Cortina tie bars are identical to the Escort part so you would end up with truly colossal bump steer.

Get an Escort MK2 rack or a narrowed Sierra rack.