Is a point inside a graphics group composed of multiple Polygons and FilledCurves, not all overlapping?

I have many thousands of points, and I want to check if they are inside a GraphicsGroup that is composed of many Polygons and FilledCurves, similar to GeoWithin but without having to make tedious cloud inquiries.

I get RegionMember Errors and besides I suspect RegionMember is too smart to do a simple 2D numerical True/False test efficiently.

I’ve done this once many years ago by counting if a line from the point to infinity crossed all of the polygon segments an even or odd number of times, but would expect Mathematica to have an function already.