DAVOS, Switzerland—Rising tensions with the U.S. are spurring new plans in Europe to do something that has long seemed impossible: break with American technology in favor of homegrown alternatives.

Almost a year ago, Nigel Farage and Zia Yusuf embarked on a ruthless internal purge of Reform UK. Active members were expelled, sidelined or smeared. The common thread was unmistakable: those removed ...