She should never have responded to President Trump retweeting the Britain First videos. A complete and dignified silence was the diplomatically correct course of action. The Donald does not forgive or forget those who cross him - and now more than ever the UK needs to make and keep friends aboard.
As for Britain First and Jayda Franken herself: props to them for the work they are doing. The mainstream of course reviles them, but what is the mainstream doing to halt the invasion of our country? Answer, nothing. At least BF are putting boots on the ground.
As for Trump, he probably had little or no idea of what he was doing; likely he has never actually heard of Britain First (which was formed when senior BNP figures argued, resulting in a schism. The BNP effectively went out of business and a couple of other parties were formed, including BF)
Trump also tweeted at the wrong @TheresaMay. However, when Trump makes a mistake he does not retract, he doubles down. TM should know this and should not have (effectively) forced him into the current position. If you play the game according to his rules, Trump will give you what you want. If you don't, then you're the enemy.