Will standing on a non-conductive surface with wet feet prevent grounding and therefore electrocution?
You can get electrocuted while fully insulated from the ground.

Power could flow through your body from one part of an electrical item to another. 

(I DO NOT RECOMMEND THIS)
For example, if you stood on a plastic chair (a very bad conductor), in perfectly dry conditions, and put your fingers into a live light socket (i.e. with the power on) you will get electrocuted with the power flowing through your fingers. If you touched the live power with fingers on either hand, you might die.
(I DO NOT RECOMMEND THIS)

It is extremely dangerous for power to flow through your heart. That could happen by touching two different live parts of electrical equipment with two different parts f your body.  

You might, for example, touch some part of your bathroom which is itself earthed, such as water pipes, a water-heated towel rail, a metal sink drain, etc, while touching a live part of a piece of electrical equipment.

Your homes electrical distribution board should detect power running to Earth, and switch off, but I DO NOT RECOMMEND YOU TRY THIS.

Summary: You can be hurt or killed without having a connection through your feet to ground.

However, consumer electrical equipment is designed to be safe to handle. They are either encased in plastic, or the case is connected to an electrical ground connection. When the case is connected to ground, and the equipment is damaged, the flow of power via the case should trip the fuse or the circuit breaker. This protection mechanism can trip even when you are not touching the equipment.

Hence I do not agree "It is a well known fact that one should not handle electrical equipment in general and electrical home appliances in particular when barefoot". I do not believe it is a "well known fact" because it is not adequate and is misleading. It is an illusion of safety.

The only time this might be true is when equipment is disassembled or broken (Edit: which is an extreme meaning of "handle"). The danger through feet is not significantly worse than through your hands/arms. Insulated boots might save your life, which would be great, but they might not. (Edit: Sitting on a metal framed chair might be as lethal). Assuming safety because of them, or because feet are not bare, is IMHO a dangerous assumption.