A stock objection to Pascal's wager is the many-gods objection. Pascal's wager is said to be a false antithesis because he made Christianity the standard of comparison. But that ignores a range of religious options.
And it's true that Pascal's wager all by itself can't be used to leverage one religious claimant over another. But whether that's a weakness in the wager depends on the opponents. If it's a debate between a Christian and a Muslim (for instance), then the wager is inadequate.
If, however, it's a debate between a Christian and an atheist, it would be nonsensical for the atheist to complain that the Christian hasn't eliminated all the religious rivals. After all, the atheist doesn't believe that any of the religious alternatives to Christianity is true. So why does an atheist suppose a Christian philosopher or apologist must first rule them out before an atheist can evaluate the choice between Christianity and atheism? If an atheist is debating a Christian who deploys the wager, the atheist has already eliminated the other religious alternatives as live options to his own satisfaction, so the atheist has, in a sense, cleared the field for the Christian.
To be sure, the atheist has also eliminated Christianity to his own satisfaction, but that just means the Christian apologist must make a case for Christianity, in response to the atheist. And, of course, the atheist has his own burden of proof.
To take a comparison, if a naturalistic evolutionist is debating an old-earth or young-earth creationist, it would be illegitimate of him say that his opponent can't make his case until he eliminates theistic evolution, for both sides in that debate think theistic evolution is mistaken (although they may have different reasons for their assessment). In most debates between two adherents of opposing positions, both sides act as if their side is the right side. By the same token, when two adherents of opposing positions debate the same issue, they act as if there are just two alternatives: the ones under review. That's generally the nature of a debate between two disputants.
Now, a young-earth creationist could debate an old-earth creationist, a theistic evolutionist, or a naturalistic evolutionist. And a naturalistic evolutionist could do the same thing in reverse. But debate topics are typically restricted to keep things manageable. You try to debate one position at a time. Suppose a naturalistic evolutionist bested a young-earth creationist in a debate. It would hardly be fair to say that's a false dichotomy because he failed to disprove old-earth creationism or theistic evolution in the course of the debate. That's another argument for another time. He still won that debate.