Save the Birds in My Pine Shrubs
Anytime when birds are not nesting would be least disruptive - so avoid doing the removal in late spring and early summer if you are concerned about disrupting their reproductive cycles.
I should add that tightly branched evergreens such as those shown in the photos are popular winter cover for many species. (I also happen to think they are very interesting and attractive).
As such, late summer up until late fall would be the best time to remove them in so far as the birds' needs are concerned. That way they will have time to find alternate shelter before winter sets in.
Just be sure you can clean up and dispose of the pine brush quickly so as not to invite disease or lure insect pests like pine borer beetles to the area. Disease and pests can sense are attracted to the aroma of broken or cut wood from stressed and damaged trees. Which is why most removals are done in winter.