i have had 14 cars in my driving lifetime, all mostly sh!t boxes millions of years old....nearly all hav had crusty old manky tax disk holders in the windscreen....not ONE of them has ever torn whan i've taken them out!

you are dealing with BMW's and Mini's which i presume are less than 5 years old so the tax disk holders should come out with ease if your careful...

i think you are just being a heavy handed caveman and ripping them out without even trying to remove them carefully - i think if you can salvage the original then DO - but if not then yeah rip it out....but seriosuly, there not that hard to take out