1986 is really the only relevant date for drop in auto sears...1981 is near useless in the wake of US v. Cash.
Prior to the 1986 machinegun ban, in 1981, BATF issued a ruling (revenue ruling 81-4 IIRC) that drop in sears were machineguns in and of themselves and thus needed to be registered to be legal. For years after that ruling, BATFE viewed those drop in sears made (but not registered) before the 1981 ruling to be legal to possess, but NOT TO USE or INSTALL in any firearm. You occasionally see this type advertised in SGN. The major problem with these under BATFE's more lenient interpretation of 81-4 is that if caught with one, the burden of proof is upon the accused to prove the sear was made prior to 1981. If you can't do that your mere possession of the sear can be deemed to be possession of an unregistered MG. Also, as Jim Keenen said, even if you were caught with a sear which you could definitively prove was made prior to the 1981 ruling and you also owned an AR15, you were also in violation of the law, the date of manufacture of the sear notwithstanding.
In US v. Cash, Judge Easterbrook correctly noted that there is nothing in the federal statutes that allows BATFE to administratively exempt a machinegun from the purview of the National Firearms Act. Once BATFE ruled that a drop in sear was a machinegun, they could not pick and choose which drop in auto sear machineguns were controlled by the NFA and which were exempt from the NFA based upon the date of their ruling or the date of manufacture. IOW if a device meets the statutory definition of a machinegun, all such items are also machineguns and thus controlled by the NFA. A machinegun can not cease to fit the statutory definition of a machinegun just because it wasn't made by a certain date. While they couldn't exempt certain machineguns from the NFA, the most BATFE could have done was to issue a tax-exempt registration of the unregistered pre-81 autosears, which would have necessarily ended on the enactment of 922(o) on May 19, 1986. In essence, the 1981 date was really only applicable for an amnesty on the tax for registering a pre-81 sear up until 1986.
Now, as noted above Cash is currently only binding in the jurisdiction of the Seventh US Circuit Court, but Easterbrook's logic is sound. BATFE clearly overstepped their authority by attempting to administratively exempt machineguns from the NFA, thus arbitrarily applying the law. My guess is that the only reason it hasn't been adopted in any other jurisdiction is simply that no other Circuit Court of Appeal has taken up the issue. When/if another has occasion to do so, there is little doubt that the AUSA will research Cash, point out the improper interpretation of 81-4, and the court will ultimately come to the same conclusion as Easterbrook.