Cheater plugs are not safe.
No, it is not safe to use a cheater plug — at least not in the way most people do.
The third prong (ground) on an extension cord exists to give electricity a safe path to earth if something goes wrong. If a wire comes loose inside a tool or appliance, the ground prong directs that current into the ground instead of through your body. That is why three-prong plugs exist.
A cheater plug (the little two-prong adapter with a metal tab) is supposed to convert a three-prong plug to fit a two-prong outlet. The problem is that the adapter only works if you actually connect that metal tab to the outlet’s wall screw — and that screw has to be properly grounded. Most people just plug in the adapter without connecting the tab. Now you have an ungrounded tool and a false sense of safety.
If you are using a cheater plug on an old two-prong outlet and do not connect the ground tab, you have effectively removed the safety feature. A short could energize the tool’s metal casing and you won’t know until you touch it.
The only time a cheater plug is acceptable is when the outlet is actually grounded through the metal box and you attach the tab to the screw. But even then, it is a hack. Just buy a proper three-prong extension cord or have an electrician replace the outlet.
Your safety is not worth saving five bucks on an adapter.