If broccoli heads are molded, does one have to throw out the whole thing?

I'd cut off the mouldy bits and give it a wash. If it smells fine then it should be ok.

off WITH THEIR HEADS

No, just cut off the moldy bit. Mold doesn't grow on places it hasn't grown on yet.

Go ahead and eat them to find out 😏

Of course not. You cut away the mold, waste of food otherwise in my opinion. As an example if you have a bad side of an avocado (which you often will have), you just cut it away and eat the rest.