"He is talking about white anglo saxons ie English. He is a celt ie a Scot"
This is totally silly. If he was talking about the English he would have said that. The term "White Anglo-Saxon Male" doesn't just refer to English people and it never has. It is being used as a generic term to describe the typical stereotype of a British or probably in this case Australian male. Likewise the pre-fix Anglo when used in a modern sense refers to Britain or the UK not just England.
By the way Bogle comes from the Scottish Borders as do I. Do you really think that 'racially' people in Cornhill are regarded as Anglo-Saxons whilst those in Coldstream just across the Tweed are Celts? Different nationality yes but it is perceived as one lot being descended solely from one set of dark age peoples and the other a different lot. It is absurd to imagine there would such a thing as someone descended 100% from Anglo-Saxons or whatever else. Plus anyway the Borders was part of the Anglian kingdom of Northumberland anyway and the dialect Bogle would have naturally spoken in his youth, and has been spoken in one form or another here for about 1500 years, is descended from an old Anglo-Saxon dialect.
Scotland is a Celtic nation yes in the modern sense that the non-English countries in these islands regard themselves as that. Celtic in that regard is not the same as being somehow racially Celtic dscended from only Celts and racially the same as the Welsh but distinct from the English. Scots are descended from Britons (both Cumbric and Pictish) as well as Anglians, Norse, Irish, Anglo-Norman, and a host of more recent arrivals.
You are looking for racism and finding what you want. The song is obviously a comical song about the loss of male self confidence in society. Nothing more.