If anything, the existence of nuclear weapons strengthens the Mandela effect argument. Consider this, there could be who knows how many unknown particles and energy forces out there, that we cannot document or detect due to our limited technology. We are only limited to human dimensions and there can be somethings existing in 5D or 6D we don't know. Physicists, everyday, are trying to seek out these new particles and energies. Now, if we can't even document these unknown particles and energies, how do we know what effect will bring when we mess around with them. This is where the nuclear weapons come in. Nuclear weapons mess with these particles and energies, which we don't even know is happening because we can't detect it. Before discovery of radiation, people used to use Tritium in cosmetics because they couldn't have known about radiation. Similarly, there could be many energies and particles we don't' know about, but we are messing around with just like the Tritium cosmetics, and it is changing everything we know.

To close your mind mind to Mandela effect is to assume our current state of science is complete, that there can be no other new unknown possibilities out there. Einstein turned classical physics on its head and now Mandela is doing the same to "modern" science. Open you mind!