I'm a bit of a fusspot cleaning bird feeders and the ground around the birdpole - but it's not so much because of the birds being infected but because a family member has a long-term illness and my bringing in any infection from the garden would be a big problem. So I always look like Mrs Fuss going out there with latex gloves on especially anywhere around the bird area.
I keep a basin and brushes etc separate for the birdie items and once scrubbed in soapy water I leave them overnight in the cleaned basin with added Milton sterilising tablets. Given that Milton is used for baby milk bottles, it seemed reasonable to use it for the bird feeders. I do it regularly and if it's been raining and I know whatever is in the plastic feeders will get all gummed up in the bottom tray - I clean them as soon as I can. The pidgeons are a huge problem as they sit on the top of the birdpole and defecate over everything.
Under the birdpole I have concrete slabs (the cheap light coloured ones from B&Q). They're just sitting on top of the lawn, not cemented in - so that I can move them if I want. I tip a thin layer of sharp sand over them and then just sweep it into a rubbish bag when things get messy. It's quick and easy - and a pile of sharp sand around also stops seeds germinating in the surrounding grass.
This has solved my problem. Might seem over-fussy, but as I say, I cant risk passing on any infection to an ill family member so I take more precautions that most sane people probably would!
I've also found that standing any rusty metal tools in a bucket of Milton for a couple of hours completely removes rust - and with a dry and oil afterwards they come up like new. Gardening madness maybe - but it works for me.