As you said, this is a super common practice in home brewing. I've never tasted plastic in my wort or finished beer.
That being said I would not put boiling water in it. I once recirculated my strike water with a pump to preheat the mash tun and it formed a bubble in the the plastic. Even in that extreme case I couldn't smell or taste plastic in that batch.
As far a infection, you boil the wort so there is no need to sanitize your Mash/Lauter tun. You will not get an infection that would survive into the fermenter. (General Cleaning is all that is needed).
Tap1 - Mosaic SMaSH Pils 34/70 (1.054)
Tap2 - Citra Session IPA US-05 (1.054)
Tap3 - Belgian Pale Ale WLP550 (1.060)
Tap4 - Pub Ale US-05 (1.060)
Tap5 - American Strong Ale US-05 (1.072)
Tap6 - Black Lager 34/70 (1.072)