Back in the day, Disney movies went in for hardcore ethnic and racial humor (think about the disgustingly racist crows in Dumbo). We already discussed Admiral Boom's racial attack on African natives in the Admiral Boom character section—which brings us to the Irish fox.
This sequence isn't really "racist," but it's oddly adult political humor inserted into a children's movie. Most people would probably miss it, it goes by so quick.
At any rate, a group of English hunters are pursuing a fox, who speaks with an Irish accent:
FOX: Faith and begorra! 'Tis them redcoats again! …Saints preserve us! Yikes!
Fortunately, Bert saves the fox, so it doesn't get killed.
This refers to the conflict between the British and the Irish over many centuries—from Oliver Cromwell's genocidal campaign against the Irish, to the later revolutionary struggle against British rule. In Mary Poppins, the talking cartoon fox is talking about that, since "redcoats" are British soldiers (the fox hunters are also wearing redcoats).
It's a heavy reference for a kid's movie, that's for sure.