The Midge sure song is talking about things that might happen in the future, but he can’t be sure that they will - this scenario requires the subjunctive tense.
Therefore ‘if I were’ is grammatically correct.
For example, Midge sings
“If I was a sailor, seven oceans I'd sail to her”
But it should be
“If I were a sailor, seven oceans I'd sail to her”
Other comments talk about the conditional tense; this is generally when you use ‘would’ or ‘could’. Note that it is used in the lyric above ie. ‘I would sail to her’. The act of sailing being conditional on Midge Ure becoming a sailor.
The subjunctive tense is often used with the conditional tense.
- If I were to win the lottery I would jet off to the Bahamas.
- I would tell her if I were you
- I could climb that mountain if I were fitter
The example "If I was being rude, then I apologise" is using ‘was’ in the past tense. This is an action which has occurred and is completed. It’s a completely different scenario to what Midge Ure is singing about.
Just as a by the way, Beyoncé uses the correct tense in her song ‘If I were a boy’.
If I were a boy
I think I could understand
How it feels to love a girl
I swear I'd be a better man