If you've got one monument and two (or many) groups using it you have a shared monument.
If they disagree about how it should be used (leave stuff/remove stuff) you have a conflict with no chance either side can win.
So, you need a compromise solution. If EHand NT weren't so wimpish and anxious to suck up to the spiritual groups in preference to everyone else they'd have put up notices saying what is and isn't acceptable at places which THEY are responsible for.
Don't hurt the stones. Don't take tealights and candles anywhere near them (duh!) and don't leave the following tat: (list).