Should I be worried about visiting rats?

Hello, I'm a new member having joined the RSPB a fortnight ago.
I moved to a rural location in northumberland last year and immediately put up loads of bird feeders. I'm enjoying so much watching all the visitors to the garden. It's part of my morning wake up with coffee.
Despite choosing feeders which hang from a single pole mount, and despite having three cats and a Jack Russell, this week alone I have seen rats visiting the front and back garden. This morning I watched one shimmy up the pole, eat from the flat feeder (for non perching birds), jump down, have a drink in my garden ponds and bolt back down his hole again. I fell like I'm putting on a full board with buffet for the rodents at the moment.
Should I be worried about hygiene? Should I be bothered by this, after all, all welcome?
If I should be bothered and worried about hygiene, what can I do to deter them or discourage them. I will not poison them nor am I prepared to stop feeding the birds. I have looked at trays to help avoid spillage but I've also seen how messy the birds who feed are, and can't see anything but giant bin lid sized trays catching all the feed they throw around.
Please advise.