I remember reading an Isaac Asimov story where aliens learned that we did all our nuclear detonation on the planet’s surface instead of on space and decide that humanity should be quarantined and not allowed into the interstellar society.
Of course living through the decades since Asimov wrote that story, it seems the aliens have plenty of other reasons to keep our species quarantined.
It's a common trope in sci-fi, but also silly when you consider the scale of space and how radioactive it already is.
And then consider that any civilization capable of interstellar travel would already need to be harnessing energies that make nukes look like firecrackers.
At some point in the far future it might make sense to renegotiate that treaty, but for now we're so far from being able to build a practical Project Orion type spacecraft that the issue is moot. And in the meantime there are other nuclear rocket designs which don't rely on explosions and would comply with the treaty. Those engines would be perfectly adequate to send manned missions to Mars and the outer planets, if we were willing to spend a few trillion dollars.