My thermal cut-off switch for my oil furnace blew and my neighbor replaced it until a tech could come out and check it when I had my cleaning. The switch blew again and the furnace tech bypassed the switch instead of installing a new one. Should a new one be reinstalled, or is it fine to just bypass it? My neighbor said its a safety issue because if it gets to hot the switch won't be able to shut the furnace off.
I would really want to know why the switch failed twice, and running the unit without all safety devices seems like a bad plan. I'd find a new tech (don't use the other guy again) to diagnose the actual problem and install a new switch correctly.
The tech may have never seen a thermal cut-off switch do anything and decided it wasn't needed, but that's not really something that should be done. Your neighbor is right - get it fixed properly.
The switch is an extremely important safety feature. If you have an oil-fired boiler, it can explode with a tremendous force, enough to destroy your entire house and kill everyone inside. https://www.google.com/search?q=boiler+explosion&ie=utf-8&oe=utf-8#q=boiler+explosion&safe=off&tbm=vid
If you have an oil-fired air heater (no water to explode), in the worst case only your house will burn down.
The fact that the switch already blew twice shows that the furnace has a serious defect, the switch might be the only thing keeping you from disaster.