I can see on the taxon page that the cuckoo has an entry under ‘Establishment means’ for the UK but the magpie doesn’t., so I guess that’s what causes it.
Why is this, and would it be helpful for me to tag some of the really obvious ones, or would I be messing things up?
I think it just mean nobody added “native” tag for them in setting for country place (if there’s nothing more linked to iNatUK settings), it doesn’t really matter much, as long as it doesn’t say it’s introduced it’s supposed that it is native, but you always can add such tags if you want to!
Use the search in the right panel to find the species or group (for example its faster to enter birds and then work with the results than search for one bird at a time).
Click edit under the species thumbnail, and choose to edit the Establishment Means, highlighted in yellow below although it doesnt show well on the dark theme, in English it says Establishment Means, then just save.