Your analogy isn't strictly absolutism vs relativism, given that your absolutist position is also simply asserting itself to be correct, but absolutist positions can also justify themselves.
Considering all paths isn't incompatible with absolutism in general
Consider a sign that says:
It's important to consider all paths. This one is the (only) correct one because [reasons].
This is still an absolutist position: it's asserting that there is only one correct path, but it's still recommending that you consider all paths.
This probably best describes the skeptical atheist position.
Atheism very much make or reject truth claims (or make claims about what's rational to believe or to not believe is true), so it's not relativist. But those claims are justified rather than just asserted.
Skepticism encourages you to explore various claims and question your own beliefs, to determine which claims are most rational to believe.
The focus is on finding a framework for evaluating claims, that can be demonstrated to be likely to lead to true beliefs (to the extent that we can know what's true). This then leads to the conclusion that we should believe some claims and not others (which isn't quite saying that those claims are necessarily true or false, but in some cases they should merely be treated as if they are).
Note the two terms: skepticism + atheism. The former is the framework, the latter is the conclusion. Skepticism is "consider all paths", atheism is "this one is correct".
* the above roughly applies to both "weak atheism" (rejecting existing god claims, but not explicitly asserting that no gods exist) and "strong atheism" (explicitly asserting that no gods exist), but more so the former.
Morality is more subjective, though.
(There may be indifference atheism too, which could be considered more relativist, but this isn't typically advocated for, because those people are indifferent.)
Considering all paths is incompatible with dogma
The absolutist position you presented sounds closer to dogma, i.e. a belief held unquestioningly and with undefended certainty.
To argue against this, I would present a slightly different analogy:
You come across a crossroads with 2 signs. They both say "This is the correct path. There is no other correct path".
If you follow the one path, you'd be going against the other sign, and vice versa.
This demonstrates the flaw in a belief system asserting itself to be correct, rather than demonstrating that.
Any belief system can trivially claim that it is itself correct.
So a claim within a belief system asserting that said belief system is correct carries no epistemic value.
Whether with this analogy or your analogy, one needs to evaluate the merits of each claim individually, and see what the justification for that claim is. It doesn't matter if this is a claim stating that "this is correct" or "the correct path is relative".
This simple analogy is a demonstration of the importance of considering all paths, regardless of whether they claim themselves to be correct.
Note: skeptical atheists are typically fine to leave theists be, if those theists feel theism is the right choice for them, as long as those theists don't try to impose their belief system on others. Atheists aren't that inclined to go and "convert" theists who are just happily living their life in peace (because, unlike with many forms of theism, there are no eternal consequences to not doing so).
Atheists will certainly hold that religious claims are unlikely to be true (considering the extent to which they're currently supported by evidence). But if you don't care about believing things most likely to be true, that may not matter that much to you. That might be considered to be one interpretation of "make a choice that works best for you".
Although the problem with leaving those with other beliefs be is that belief systems influence one's morals, and those morals influence the laws you'd support, so it's hard to avoid imposing that on others. This is especially true for religion, which often has rules that have no justification beyond "my god says so", so it's hard to reason about that, compromise, or find some solution that's in everyone's best interest. Those rules often include what people are and are not allowed to do in the privacy of their own home, even when that isn't hurting anyone else, which is especially problematic to impose on others with different beliefs.