The licence specificity states;
This licence permits landowners, occupiers and other authorised persons to carry out a range of otherwise prohibited activities against the species of wild birds listed on the licence. This licence may only be relied upon where the activities are carried out for the purposes specified, and users must comply with licence terms and conditions. These conditions include the requirement that
the user must be satisfied that legal (including non-lethal) methods of resolving the problem are ineffective or impracticable.
THE PURPOSE(S) FOR WHICH THIS LICENCE APPLIES
1. Subject to paragraph 2 and the licence conditions,
this licence is granted to:
(i) Conserve wild birds, and
(ii) Conserve flora and fauna.
To argue for the removal of bird feeders for other species would be to argue against that which is logical never mind practicable.
It is not logical or practicable to remove a source of food for other wild birds when all you wish to do is aid those wild birds conservation.
It is for the purpose of the wild birds conservation that shooting magpies is permitted under the terms of the licence.
Feeding other birds cannot be the problem (IMHO) as attracting other species to the safe harbour of your garden to propagate and flourish is their purpose - feeders are not there as a bait for magpies, but as a conservation means for other species.
I have had a good read of the "Act" though I will freely admit I might have missed the glaringly obvious
but I can't find anything that says otherwise.