The problem with the followers is they will call you ignorant, arrogant and idiot, if you criticize their idol. (No offense, just an analysis Because I was like that too.)
I'm not against inviting Muslims and others. Do invite them, let them know the beauty of Sanatan.
But it doesn't mean if a muslim visit a temple, the pujari should stop worshipping the deity and start to do Nawaz.
Now let me tell you why the song Ali muala and Raske kamar was inappropriate,
Allah or Ali Maula said in Quran:
Kafirs should either be forced to accept my ways or should be slaughtered, whereas their women should be taken as slaves.
Allah said Women are fields of men.
Allah said the earth is flat.
Allah said one who doesn't obey me will burn in inferno.
I think these points are enough to make it clear Allah or Ali Muala is not Shri Shiv or Shri Ram.