Religion is the word we use to describe how us human's have managed to twist and warp and misunderstand that good news. We use it for gate keeping: "sorry this event is for church members only". We use it to put down people based on their behavior: "He seems like he needs religion". We use it to interfere with the law of the land: "Sorry, that law doesn't apply because of religious freedoms". And so on....
I don't think the big man gives one fiddly flying fig leaf about "religion". His son said(over, and over, and over!) that "I desire mercy, not sacrifice.". That means NOT excluding people over religion, insulting or belittling them with religion, or creating an unfair situation with "religious freedoms" in law. He wants MERCY.... that means instead of telling the beggar that religion would help him get clothed, fed, and generally happy - you should be giving him or her your clothes, sharing your food or drink, and welcoming them to your home where they can be safe. Will they abuse your trust? Who knows - and it's not important - your mercy to them was the critical action. You don't get into heaven for being discerning and clever...there is no award for actions like "I didn't invite him home, because he looked like a criminal and I don't trust him...". That's not mercy, that's you finding a human excuse to ignore the least of your brethren.