I see nothing wrong with seperating individuals. But if someone decides to ignore you and forces you to ignore him too (since you can't do anything about it), it means a cut of your own free will. It's not up to him to make decisions for you. And actually, what sounds so awful about a GM intervening the situation? That's one of their jobs, after all.
What can a GM do for me?
# Assist in keeping the player free from unwanted harassment.
I'll try to give a practical example on how it could be handled.
Player XYZ annoys you with following you where ever you go, yelling at you and running through your character. In other words, he is really dotty about you. You try to get rid of him. At first, calmly. You tell him to stop that. He continues. You tell him to move along, or else you will call higher authorities. He continues, because he will just be going to behave properly for if you really do. At this point, some people are so annoyed, that they choose to challenge him. He declines, then continues. Final solution, you are going to ignore him, totally, because his harrassment is not restricted to only his voice. You type in: /ignore_totally XYZ. A confirmation box pops up for XYZ. He quickly reads it, then laughs and clicks on 'No'. He continues.
What he doesn't know: By clicking on 'No', a GM will be sent the chatlogs of the last 5 minutes and the next 5 minutes, just like with /report (in case there is no GM on, it could be read up later, and then dealt with the situtation). But if a GM is on, he will now contact you. You tell him that you are being harrassed. He asks for your location and you answer him. Being invisible he comes to your position and witnesses the delinquency. With this proof, he can put you two on eachothers ignore list. Problem solved. And with a GM being the one who had the final word on it, this feature will not going to be abused in any possible way.
It would be something different, if both players agreed to the full ignore, but both at least need to have a chance to defend themselves from this feature, and their possible abuses.
As for the 'LA LA LA, I CAN'T HEAR YOU', such beings are best dealt with by /report, as such a sentence is clearly OOC and disturbing not only you, but also the people around you.