I'm unconvinced alien technology would shake anyone - we're pretty good at incorporating new tech into our lives.
Case in point, less than a decade ago when I told my then preteen niece and nephew the internet basically didn't exist when I was their age, they literally did not believe me. The internet was so fundamental to how they lived they could not conceive of a world without it, even though it just existed as newsgroups and email (if that) when we were all born.
In reality, if wild alien tech showed up en masse, we'd spend the next 10 years rewriting our physics books and college research projects, the next 5 to 15 years monetizing the hell out of it, and the next 10 to 20 years awkwardly rewriting our legal codes to (badly) deal with the consequences. But in 25 years, kids could not even conceive of a world without it.
As to the religious aspects, Buddhism is still around despite Christianity, Islam, etc. arriving on the scene. Would some people adopt alien belief systems, if any, especially if said aliens had actual evidence for their validity? Sure. But all out existing religions would keep chugging along, albeit likely with less believers.