You do not have the right to decide how much their religion did or did not influence them Why not? You are!.
Let's get this true christian and true muslim out of the way.
There are versions of every religion. There are huge numbers of people who follow a different Islam or a different Christianity. They abuse or kill gay people or unbelievers and commit other atrocities too numerous to mention.
You can tell me that is not how it should be and produce verses to prove it, but that doesn't alter the reality.
You may be sure yours is right, but none of you own the copyright so they are just as 'right' as you are. Feel free to complain to them about it, not to me.
Maybe you are nice and your version is gentler. If so perhaps you could come to some arrangement with them so you can have a different name and holy book. I don't say you must, that's entirely your affair.
In the meantime religious people will continue to do evil things and justify it by saying that's what Allah or Jesus wants them to do and I will continue to criticise them.
I will also cast doubt on any of you having the truth since you can't agree on what the truth is.