Splitting the infinitive

Why, oh why, does this annoy me? Why does it even get to me and why do I recognise it wherever and whenever I hear or read it ...? The damn split infinitive.
You are probably thinking - why is she 'going on' about this? I am watching the television, - a news programme has just finished and I have heard the news presenter use another one....
I am reasonable at grammar. Not outstanding, by any means and certainly I am not someone who has studied grammar or even (unfortunately, and a great disappointment to me) someone who has a degree.. BUT... I do recognise a split infinitive. At fifty paces. This is because of my dear, late, maternal grandfather - Montague Plascott. Just his name sounds dignified I think and it is because of him that whenever and wherever I am when I hear one I think ... OOOOH, OOOUCH.. not right! It was his absolute 'bete noire' and he taught me to recognise them as "Bad Grammar.. " - at times I really wish that I didn't. Maybe it isn't recognised anymore as 'wrong' and maybe English teachers do not attach great importance to this. I will ask my BN who teaches English to 17 - 18 year olds.
Let me give you a very famous example...
"To boldly go"....... (Star Trek style).
And some other ones.... " To blindly feel" or "To beautifully sing" .... In each one as you will see that the 'to..... do something'... i.e. in the last three examples..' to go', 'to feel', and 'to sing' is the infinitive and it has been split in the middle by (in the examples above) - boldly, blindly and beautifully.
Perhaps it doesn't sound so awful. Perhaps it is only because of my grandfather that this little point of grammar still sounds so wrong when I hear it ...In some ways that is rather nice...
At least it means that after many many years he is still very much 'alive' to me. He died in 1975.