So the consequences on Earth are somewhat easier to see, as it is mostly just about having cheaper energy. The most obvious downside back on Earth is that climate change doesn't have an easy solution, but we can probably fix it with a mix of renewables and energy storage instead(and it might even be cheaper regardless of whether fusion is possible). The problem with climate change is more economics than it is physics. One possibility is that this could also serve as a means for additional space development using space based solar. While the economics don't currently work well, this could change in the future if energy demands increase without better alternatives.
Anyway, the main interesting problem is about what this does to the possibilities for space colonization. Even going to Mars long term becomes much harder when the best energy sources are nuclear fission or solar. Anything past Jupiter is likely off the table because the energy would get too expensive. The JUNO probe is the first to use solar that far out, and it was much less efficient as a result.
What options might be possible as other alternatives to fusion power for space colonies? Would it still be plausible to have extrasolar colonization at all without fusion power?