What other major religion claims that people on other paths are doomed? The traditional example I have heard is Islam, but actually Islam thinks other Abrahamic religions are valid. Islam's hell is based on bad behavior - not choosing the wrong path.
That's not actually correct.
Islam considers itself to be Abrahamic religion 3.0 and considers 1.0 (judaism - moses) and 2.0 (christianity - jesus) to be the valid ancestors of islam.
When it says that Jews and Christians, the "people of the book" are 'safe', it is actually talking about jews
before Jesus came on the scence and christians
before Mohammed saw the light of day.
Jesus, in islam, is considered a very important prophet.
The current christian belief about Jesus, that he actually IS god, is considered blasphemy and idolatry in Islam.
Jews and Christians are actually only tolerated insofar as their beliefs actually line up with islam. So essentially, it says that Jews and Christians are "safe" - as long as they believe the islamic version of abrahamic religion. Which is just to say, they'ld have to be actual muslims.
A christian who says that Mohammed is not a proper prophet, is not to expect any mercy when facing Allah.
The general islamic perspective is that judaism and christianity were valid "revelations" of the true god, but that both those revelation got
corrupted through time and that what jews and christians believe
today, is thus not the "true" religion, but a corrupted version thereof.
When it says that jews and christians are "safe", it is talking about those jews and christians who believe in the
non-corrupted original version of those religions. And, from the Islamic perspective, not a single Jews or Christian alive today, follows that non-corrupted version, because it simply doesn't exist anymore.
Well... no, actually, it does still exist. Muslims call that non-corrupted version "Islam".
Having said all that.... I'm not aware of any religion that has a concept of hell/heaven, where one can manage to be admitted to its version of heaven,
without doing what needs to be done
according to that religion to be admitted in that heaven.
EDIT: This might seem similar to Pascal's Wager, but it is fundamentally different. It is about walking more than one path - essentially hedging. No matter which path is true, the Christian's butt is covered. If Hinduism/Islam is true, the Christian with good behavior is just fine
I just explained how that is not true.
According to Islamic theology, not a single christian alive today meets the criteria.
One problem with this approach is that Christianity often is understood to require faith/belief. However, faith/belief can sometimes be cultivated through desire and practice. The other problem is that a person must consider Christianity's concept of salvation plausible enough to consider. I find that my faith in Christianity is about zip due to my belief that the historical Jesus did not teach Christianity.
For me it's easy... I don't believe because I have never been given a rational reason to believe.
Having said that, what you describe turns christianity into self-contradictory nonsense. If the God of the bible is indeed "benevolent" and "all just", then he would NEVER let rewards or punishments depend on mere beliefs, regardless of behaviour.
A system where a believing mass murderer can obtain eternal bliss while a non-believing dedicated charity worker gets eternal punishment is about the most unethical, unjust and immoral system I can think of.
By that fact alone, I can dismiss the entire thing as nonsense.