The legalities of tape trading hasn't changed since the pre-You Tube 90's.
Most people that are serious tape traders retain a code of basic ethics/morals; i.e. not trading stuff that are commercially, domestically, and easily obtainable otherwise...The Golden Rule is always If The Companies Producing the Entertainment Would Lose Money Because You're Trading It and Not Buying an Actual Product, Then Don't Go the Trade Route. If you maintain that basic spirit and honor each transaction as two individuals trading material of basically equal value between each other, you don't have anything to worry about.
Actually what's nice is because of the proliferation of YouTube and other media sharing outlets, people who still do tape trading are the ones who are serious about it and are much more apt to play by the rules and do things right.
The other advantage is YouTube et all is a far more questionable practice in regards to copyright issues and loss of profits...unless the company behind something is super aggressive with having stuff removed, practically everything and anything can be found on YT or other similar sites - so much so that tape traders aren't really on anyone's radar or anyone's concern. "Real" tape traders don't really have anything to worry about...those that are total professional pirates deliberately and purposely engaged with making and selling bootlegs for a profit are of course a whole different story!
But yeah, two fellow fans exchanging an unreleased on dvd 80's episode of Sesame Street for a couple of Muppets on talk show appearances really don't have anything to worry about.