Normally, this is what would you would see if you magnified older newspaper images printed in color. (check the background of the attached image)
What is this filter called? How can I recreate this filter in GIMP or Photoshop?
Halftone effects in Gimp come with quite some variety for adjusting to personal needs. From the Filters > Distorts > Newsprint... settings we can see that the resuting halftone image is better than the one posted in the question. Therefore we probably have to add additional filters. That's where creativity is asked, as there is not a prebuilt singular filter to do this.
Now this is how I tried to recreate the image above in Gimp:
0.20for R, G, and B)
Add halftone effect (Filter > Distorts > Newsprint) with the following settings:
Add some blur (which might have come from down-scaling of the image in question)
Image source: Wikimedia
Filter > Pixelate > Color Halftone...
In Illustrator you can use the Photoshop Effects (in the Effects menu) for the same thing. There are third-party plug ins for Illustrator to apply halftone effects which work a bit better than the built in raster effect. Phantasm is a great one.