Can anyone tell me how I can avoid this?

When I mounted splash shields on the table of my R2E4 (cast acrylic, and
VERY prone to cracking and "spidering" from holes), I drilled the holes
in the plastic to accept a grommet. IIRC, the holes were 7/16". I don't
even want to have special bits around for plastics, so I drilled them way
undersized, and used a tapered reamer to enlarge them without cracking
the plastic.

The grommets were made for whatever hole size I drilled, and themselves
had a bore of 1/4". The 1/4"-20 screws with a washer under the head fit
just loosely in the grommets. When you squish 'em a little, the hole
swells shut, and it holds firmly to both bolt and plastic, without any
tendency for the plastic to be stressed at the union. Unless you use a
shoulder bolt, you'll have to put a bit of threadlocker in the screw
hole, since you cannot tighten the bolt too far without undoing the whole
purpose of the exercise.

LLoyd