In a fantasy world filled with magic and miraculous beings, will the religious concepts of the locals be completely different from the human of Earth?

[Jfdlsjfd]

So when you said that "the net effect would be that people would participate in the rituals with even more enthusiasm." the people you were talking about is limited to only high level clerics and not other people?

The beneficiaries of such spells would. If the rather low level NPC Priest of your village can cast 7 Cure Wounds a day, a spell that can nurse your 1 HP-left child to full health instantly, you'll probably worship the god responsible for him curing even if you're not, right now, in need of cure. His god or church might not want to cure unworthy people after all. So while you'll happily go to the priest to have prayer said when your child is half-dying, you'll also accept to sacrifice a chicken to the god before (or after).

The existence of non clerical magic and non-deity magical beings I think would be a pretty big impact on how people thought about the importance of clerical magic and gods in a D&D world and how religion would be affected because of the two.

I don't think so. Most people would just call wizards priests of Mystra/Hecate/Isis. If you can cast spell because you're doing prescribed rituals allowed by Mystra, you'll have a hard time explaining and convincing people it's different than what the priest of Lathander, who is casting spell because he's doing rituals prescribed by Lathander, is doing. Especially when non clerical magic depends on Mystra being alive to tend to the Weave to work correctly.