Not according to every Christian I've ever known.
Guess we haven't met, then, huh?
Actually, I suspect you are painting with a broad brush .... most religions don't differentiate between your God or my God. Their differences are in methodology - do you baptize, do you not - do you circumcise, do you not - do you confess your sins thru a priest, do you not -
My 'religion' falls into a much larger category - Christian - but I practice the tenets and techniques of the Catholic religion. That doesn't make Baptists, or Lutherans, or (OMG) Presbyterians, any less Christian - it is only the method and tenets that vary. All of us believe in the same God.
Christianity stresses the point that He is the " .... one true God ...". Nothing in that statement should lead you to believe that He can't be the "... one true God ...." for those who worship with a different methodology. He has brought His message to His people - who's to say that he hasn't used multiple conduits? You call him God - Muslims call Him Allah - and the Holy Sphincters call him George. Nothing makes those diametrically opposed.
Now - ask me.
Is there only one God? Yes. (A statement of fact)
Is there only one religion? No. (A statement of fact)
Is there only one religion that does it right? Yes.(A statement of opinion)
Is it possible that God has shown Himself to other peoples in a different personification? Yes. (A statement of fact)
There. Now you've met one. Nice to meet you.