Are there any ILS approaches in Class E airspace? When descending on an ILS you can descend to 100' above the TDZE if you have the approach lighting system in sight. Cody Johnson wrote an article explaining how one pilot mis-interpreted what the rules allowed him to do, descended below 100' when there were obstructions in the way and crashed into a hill. (https://iflyamerica.org/misunderstanging_part91.asp )

Section 91.129(e)(3), Operations in Class D Airspace, is also extremely applicable in this accident. It says, 'An airplane approaching to land on a runway served by a visual approach slope indicator shall maintain an altitude at or above the glide slope until a lower altitude is necessary for safe landing.'

Class C and B incorporate Section 91.129(e)(3) by reference, so the rule applies in that airspace as well. It doesn’t specifically apply to operations at airports in Class E airspace.

My question is are there any ILS approaches in Class E airspace? Is there a a rule that prohibits them, or conversely, only allows them when there is a tower?
There are plenty of ILS approaches in Class E surface area (e.g. KCLM, KHQM, KPWT). In fact the presence of an ILS will usually require that some kind of controlled airspace extends to the surface. For an untowered airport this means a Class E surface area.