There is a trick! That only works for hatching and hatching likes. You dont actually need to design your hatch as a square you can design it as one line and then one square with no strone or fill to model the gap. And then use the alt rotate dialog to rotate your pattern only.
Whats the benefit? Well the benefit is that since you only make one line you can ...
If your goal is to use a cutter, then patterns won't work. Instead it's probably better to create the lines yourself manually, using a step blend. Expand the blend, ungroup it. Then add your shape on top, then use the Shape Builder while holding down Alt to physically remove the overlapping lines.