I have many threads running in my C# application and each of those threads accesses a
System.InvalidOperationException: Cross-thread operation not valid: Control 'myTextBox'
accessed from a thread other than the thread it was created on.
CheckForIllegalCrossThreadCalls is like complaining that you get hit by an airbag when crashing your car: the correct solution isn't to remove the airbag, it's to avoid crashing the car.
You simply shouldn't be making UI updates from the wrong thread. You may get away with it most of the time (having disabled the check) but that doesn't mean that it's a good idea - it leaves you open to subtle errors which will only show up occasionally and be really hard to track down.
So yes, use
BackgroundWorker etc to marshal to the right thread for UI access. That's why those calls/types exist.