The big difference here is that we have religionists telling me, the one who wants to build the bridge, that their way is best with absolutely no proof behind the claims. With your example, you can lump all the mysticists under Answer 1 who would build it out of matchsticks if their holy book told them that was the correct way. You can lump everyone else under Answer 2 because that answer has only sound engineering behind it, no mysticism.
You are a little too hung up on "provability" though. In the case of the bridge, it is nice that we can "prove," through mathematics and engineering, that the bridge will stand up to use. However, a flaw in the steel, or a cavity in the concrete, would render this "proof" useless. What we really need in this case is not provability, but a sound bridge.
So when it comes to issues of life and death of the spirit, how can relativism take hold? Perhaps you view all religions as equally INvalid, rather than equally valid. This is your perogative, but at least you might be honest about it. If you believe that there is no spirit and no eternity, that is not relativism, it is as absolute as an fundamentalist christian. If you aren't sure what's true, that isn't relativism either. Relativism is a denial that there is such a thing as truth. From what you said about the bridge, you have already as much as admitted that some claims are more true than others...
As with a bridge, don't confuse truth with provability. The existence of unprovable truth is something that you must learn to live with, not to scoff at, unless you are prepared to throw mathematics out the window as well. And then how would you prove that a steel-reinforced bridge would stand?
Actually, the soundness of a bridge can be tested without any mathematics. Just drive over it. If it is sound, it will support you and you will safely reach the other side. If it is not, then it will collapse and you will perish. All the proofs in the world will be of no use to you then.
And it is the same with the very real issues of the eternal and spiritual. (The issues are real, even if there is no eternity and no spirit.) The ultimate test of a religion or philosophy will come when it is time to "drive over the bridge"—i.e., when you die. At that time, all the proofs in the world will be useless to you. Your bridge will stand or fail, and you will be safe or you will perish, according not to clever "proofs" but according to whether or not your "bridge" was sound.