There are many religions who honor and worship ‘A’ God. The problem I see gaining more traction than it should, of recent, is this universal opinion the Christian God is the same for all faiths and that just simply isn't the case. There are many counterfeits and imposter's out there...unfortunately so many fail to recognize this when coupled with the universal thought we all need to get along and come together. That is not what God taught nor has He desired it be so. This push to incorporate all faiths as worshiping the same God is not for the good as you know. Am very concerned how Catholics and Mormons and other faiths are snuggling up to Islam...as if that snake won't bite. Reminds me of that story where a young girl picked up a snake and carried it up the mountain, with the promise it wouldn't hurt her...when he did bite the girl brought up his promise and why did he do so...It said...."You knew what I was when you picked me up".
You are right. Just because a Church speaks of Jesus, grace, faith, atonement, etc. does NOT mean they are speaking of the Christ and His finished work of the Bible. Even the “Bible” can mean other things to other religions. It can be a very confusing situation unless the word of truth is rightly divided, and scripture is compared to scripture. NOT traditions or doctrines of men.