I have never heard that people think fusion is impossible. It looks more like a flight to the moon appeared around 1960. You know it’s possible but there is a lot of engineering needed to make it happen.
The problem is it's not even known whether the engineering problems can be attacked at all, unlike the Apollo program where even though a large amount of work (Breadth rather than depth this time) it was an iterative evolution of past programs.
In 1960 they had no idea how rendezvous in space or a lot of other things would work but they knew they would figure it out with enough time and money . From whatever I have heard about fusion I have never heard about doubts about feasibility. It’s about trying out different things and getting experience since the knowledge in plasma physics is so thin.