Covering only one of two types of objects in a cartesian space using minimum number of rectangles
This sounds like the minimum rectangle cover problem. 


  Given an orthogonal polygon with holes, find the minimum number of
  rectangles needed to cover the interior of the polygon without
  covering any of the holes.


In your case, the red points mark the holes, and the blue points mark the interior of the polygon(s). In general, two blue regions might be disconnected, but then the minimum equals the sum of the minimum covers for the two disconnected regions. 

Your problem can be easily mapped to the rectangle cover problem, and conversely the rectangle cover problem can be mapped to your problem assuming that all vertices of the polygon are on a grid, which can be assumed w.lo.g.

The bad news is that the minimum rectangle cover is NP-hard. It's also fairly hard to approximate in general (the best current approximation ratio is $O(\sqrt{\log n})$. However, if you had more information about the red and blue points, it's possible you might fall into one of the many special cases of rectangle cover that are easier to solve.