When one follows a faith there are several basic notions included in that following. One of those is the assumption of truth. It may be dogmatic and narrow-minded, but you create a bit of a dilemma if you suggest with any faith that it is not the true religion thus there could be an alternative.
You are right in what the consequence of this usually is, and it is an unavoidable consequence. Christianity (perhaps even all the splinters of) will claim their faith is true. Same thing of Islam. Same thing of Judaism. Etc. It is not that your 3rd option is impossible, but it stands to reason that when that option is selected you are talking about a follower of some faith that does not completely buy into all the tenets of that faith in totality.
You brought up Christianity. I would be interesting to see a Christian offer room for their religion to not be the true religion as the entire basis for Christianity is a "relationship with God based on trust and faith." Usually in the context of through Jesus. Why would that same person turn around and say "but we may not be right?" Christianity suggests that Jesus himself claims to be the only way that we can be right with God, use John 14:6. "Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me." (King James Version.) In that context, under Christianity, Jesus actually claims that he is the one in whom you must trust and who teaches the one true faith. A relationship with God through Jesus. There is little room in that interpretation for a Christian who holds those words as true to offer that there is no such thing as true religion. And all of this is just one example from one passage in a context.
It also stands to reason that Islam and Judaism have similar contexts for words they hold true only to suggest their faith is also true. Why would any of them who hold these texts as true offer that their religion is not the true religion?
Appreciate this argument coming from a non-believer, and agnostic but who has studied this.