Your line of reasoning assumes that faith is completely and utterly blind, without any role whatsoever for logic and reasoning to help discern what is actually true.
Islam, Christianity, and any other belief systems aren't just binary propositions floating in a void. They are intricate truth claims of an immense nature, that purport to have the full answer to every aspect of *being* itself.
With that in mind, whe we encounter such a systematic truth claim, there are many ways we can evaluate it. For one - is it internally consistent? Do all the precepts of that system work in perfect harmony (as they claim to), or is that system self-contradictory at some point? Secondly, we can also examine whether the claims of that system are able to provide a coherent explanation of the universe outside of the immidiate bounds of that system.
Now, we have to be willing to give a great deal of charity when we examine these claims. We should assume their presuppositions are true to the fullest extent, and follow those to every possible end, so that we may have a full understanding of what is actually being asserted. Now, this isn't always easy - Christianity, for instance, is first and foremost an experiential faith, and we Christians would assert that far more is understood about God and the Church by actually *living* the faith than can be understood by mere study. But both are aspects of the whole faith.
We do not arbitrarily say that anyone who is not exposed to true Christianity is automatically damned, it isn't that simple. There's a lot more nuance to it than that, without getting too much into the details.
But ultimately, my point is that if you were to encounter a priest and an imam, there's nothing stopping you from examining the claims they make in detail. But again - charitability is key here, dismissing things without a genuine assessment leads you nowhere.