This is mostly about game logic, where I can understand the reliance on floating point numbers. I've also seen these epsilon comparisons in code that had nothing to do with game engines or positions in continuous space, and it has always hurt my eyes.

I think if you want to work with values that might be exactly equal to other values, floating point is simply not the right choice. For money, use BigDecimal or something like that. For lots of purposes, int might be more appropriate. If you do need floating point, maybe compare whether the value is larger than the other value.