I wouldn't recommend using red Loctite either.
I personal wouldn't trust pipe tape to do much locking, especially when trying to prevent a screw from moving if it has a moving part working against it. But, it will tighten up the thread fit, if it is loose, and increase friction helping prevent loosening, just not to the degree of a thread locker. It is intended more for sealing the threaded joint and does help prevent seizing, corrosion and locking up from those conditions. Other liquid thread sealants do about the same thing.
I have some experience with fasteners in motion, high vibration, and corrosive environments and have adopted the philosophy that most all threads should either be installed with thread lock or anti-seize compound (I use pipe tape on pipe threads too unless there is a contamination issue).
Thread lock really works great if you prep and apply it right. I use a thread lock (like Loctite 243) on most threads, except for some things with critical torque values where it is not recommended as it can cause invalid torque to be applied due to its lubricating properties while it is wet. I use it on boats, RC helicopters and airplanes, real airplanes and helicopters, motocross bikes, bicycles, cars, lawn equipment, etc. In addition to preventing a screw from loosening from motion or vibration it also seals it up preventing moister and other corrosive agents from getting into the threads and helps prevent dissimilar metal corrosion, electrolysis, as well as galling between the two threaded materials. This is especially important when working with steel and aluminum together. Most of my threads in metal either get Loctite, or if they don't need locking, I use anti-seize compound. I really don't like it when threads come loose or if I can't get them out when I want too. I usually think of anti-seize as the product to help get the fastener out later, but a screw put in with thread locker can be a lot easier to get out later then one that is corroded in place.
I would normally only use red for the side of a stud you never want to take out or the outside of a Helicoil.
Sounds like you have oil contamination to me too. A little oil film will really mess up Loctite's locking ability. Thread lockers work by crystallizing between the threads and engaging in the pits or roughness of the two parts.
Anything that removes the oil contamination will work.
Some solvents dry faster then others. Acetone drys very fast. It also dissolves old Loctite if you work at it. Alcohol doesn't. I have used Acetone, MEK, motor cleaner, electric contact cleaner (make sure it doesn't have and lube in it), alcohol, etc. They all work well. Electric motor cleaner or contact cleaner in an aerosol works great as it also floods and blows the oil away as well as drying quickly.
Let thread lockers cure properly. I probably don't let it cure as long as you are supposed to before putting into use, but that is another bit of good advice. If you turn it before you get full locking strength you break up the crystals and loose your locking strength.
You get about 50% of the locking strength in 30 minutes to 3 hours depending on the thread fit. You can cut that in half with a little heat. An accelerator is also available. A little moisture applied outside the joint also seems to accelerate the curing process much like it does with super glue (like spraying the ends of the joint with a little water mist, wiping a little spit on it, or just breathing on it like when you polish an apple).
Hope that is helpful
Gary