Martin Luther's bizarre interpretations (to which you refer) can be written off. Whatever he says is going to be charged with anger and a flippant disregard for the intent of a scripture. His doctorate is legitimate, however he abuses it. This is the man who causes people to be tortured for disagreeing with himself, their testicles pulled off with red hot steel, and he prefers Jews to be dead. He's no standard for scripture interpretation. Some people just have no regard for others, and he's one of them.
Using "Saved by 'Faith' not b 'Works'" he managed to take advantage of a groundwell of disapproval with the church of his day, for his own gain. He translated the scripture a particular way for the lay people to make them believe he was a prophet, but he was no prophet. The excesses and failures of the church were real, but he simply used this for himself to make himself a church that followed himself. His misinterpretation of the verse was whatever he found convenient for his purposes. It was a way to carve out a church for his own name, and I am not saying that as some catholic guy. I'm just stating the obvious. I've never been catholic, and I have no family in that institution. He was a bad dude.
That being said I realize that to this point I have not interpreted this verse for you. I merely state that I disagree with Luther. I do not believe that "The bible says the opposite," not in Ephesians even. I can see how easy it is for Luther to translate it so that it leans this way, but he's not to be trusted.
Now I will explain the verse, and now I will answer. To begin with your focus upon believing "Key claims" seems irrelevant to being a Christian. They are not relevant in my opinion and based upon my understanding of the standard canon. The verse is about faithfulness. It is contrasting works and faithfulness, but Luther misconstrues this to manipulate it into something convenient for his purposes.
I understand that large numbers of people are under sway of Luther.
As for whether there are Christians that are not true Christians, there is only the test of spiritual characteristics. These are what matter, and so I partially agree with you that there is not a specific test. There is personal growth as people improve, but there are also people who never improve. And there are people like Martin Luther: murderous and self seeking individuals that boast about how spiritual they are when they actually are more like noxious pests. Now in Luther's case perhaps he had a good side, but he was somehow quite murderous and conniving as well. I cannot count him as a peaceful man nor as any sort of spiritual person.