With the best tyres on the front, in a panic stop the front end grabs and the back end tends to loose grip. It only takes a little bit to start the back end skidding around to the front so you are looking where you have been and can’t see where you are going. Stick with the best in the back.
If you have a tyre that is bad enough to be a blow out risk, please part that car until you can save up enough to get proper safe tyres on it.