The problem with putting a screen in the intake is that as the air speed increases, the holes in the screen have to grow larger, or the screening serves to block off air flow.
At 600 miles an hour, even 4x4 fencing would be nearly the same as a plywood sheet, solid.
All we can do is make the intake compressor blades as strong as possible and calculate the statistical probability of FOD.
Mach 5 plus inter-cooler for hybrid turbo-rocket intake.
https://sci-hub.tw/10.1016/j.actaastro.2009.11.010