In theory, to some extent. But it's mostly an academic argument. The power plants that are currently in use that people are protesting against do not recycle their waste.

This argument feels a lot like you are just passing the ball to the next generation. "Hey kids, we used up all the uranium for cheap power and left you with caves full of radioactive waste. But don't worry, you can recycle it!"

As for the dangers of nuclear vs. gas, the big difference is where the danger is. Nuclear power plants bring the danger close to the population, and people just don't want that.

And finally, another issue that noone appears to mention is that electric heating isn't very popular here. Most people heat their homes with gas furnaces, so even if we'd switch to nuclear power we would need to replace millions of furnaces and massively expand the electric grid. (This is slowly changing. Lots of new homes use good insulation and electric heat pumps for heating instead of gas, but it's not something that can be easily retrofitted in existing homes)