Yes! I thought I was the only one. 3.0 year old DS has done this for about 6 months. Sometimes it's horribly embarrasing - if I ignore him he gets louder and louder, and will shout things like "Mummy don't talk to that lady [even if "that lady" is someone he knows well]. I do NOT LIKE that lady. I am FRIGHTENED of that lady. Mummy, please ONLY TALK TO DS" etc etc. When it's bad it makes it almost impossible to have a conversation. He does this with my friends, random people in the street, waitresses, people on the tills in shops, the doctor, health visitor etc, and sometimes even his father and grandparents.
To be honest, this has been my biggest parenting challenge to date. It was so bad at one point that we just stopped going places / having people over, and I started to feel quite cut off. Fortunately he is much much better now - we've been out for coffee and lunch today, and round at friends this afternoon, and he hasn't made a fuss once.
What I found made a big difference was encouraging him to interact with people we met. So in shops, I now ask him if he wants to pay, and let him talk to the person on the checkout, or order his own drink in a cafe etc. With friends I try to include him in the conversation, so e.g. I will say "DS, can you tell Xs mummy what we did yesterday?".
I do appreciate that this might be a bit wearing for the person we are talking to - obviously this means that it's still hard to have 'adult' conversations, and I am well aware that we need to move him on to the "not interrupting" stage. But for me it was just so awful that anything was better than a public screaming tantrum (which is where we would have been if I just ignored him). For us it also coincided with the arrival of DS2 and a couple of other traumatic (in toddler terms) life events, so I didn't want to be too harsh on him - it was obvious why he suddenly felt the need for undivided attention.