Officially, major religions do claim exclusivity. E.g. Buddhism teaches that it provides the path to liberation from suffering through the enlightenment found in Buddha's teachings.
In practice, some Buddhists believe that Jesus is also a way to the enlightenment. Wiki:
See also What would happen to people who don't acknowledge the true Jesus?
In practice, some Buddhists believe that Jesus is also a way to the enlightenment. Wiki:
While claims of exclusive truth are present in the world's religions, individual practitioners may embrace pluralism—some more, some less.Some high level Buddhists have drawn analogies between Jesus and Buddhism, e.g. in 2001 the Dalai Lama stated that "Jesus Christ also lived previous lives", and added that "So, you see, he reached a high state, either as a Bodhisattva, or an enlightened person, through Buddhist practice or something like that."
See also What would happen to people who don't acknowledge the true Jesus?