In the US reprocessing of civilian nuclear waste was stopped not for technical reasons, but for political reasons. The primary reasoning was that: US reprocessing of civilian nuclear waste would encourage other non-nuclear weapon states to build nuclear reprocessing capabilities which would make easier access to plutonium - nuclear weapon material.

"On April 7, 1977, President Jimmy Carter announced that the United States would defer indefinitely the reprocessing of spent nuclear reactor fuel. He stated that after extensive examination of the issues, he had reached the conclusion that this action was necessary to reduce the serious threat of nuclear weapons proliferation, and that by setting this example, the U. S. would encourage other nations to follow its lead."

https://www.pbs.org/wgbh/pages/frontline/shows/reaction/read...

Commercial fusion reactors could be used burn (transmutate) long-term transuranic waste, on the other hand they will produce short-term nuclear waste, like neutron activated steels.