Yes, I act differently around different people. But it's not because I am fake. It's because I have a different comfort zone around certain people.
We are all different. We all have different thoughts, different opinions, different agendas, different senses of humour, different idiosyncrasies.
What you do with some people you wouldn't do with other people. I'll give you an example, you wouldn't swear like a sailor when you are around your grandmother, right? You modify your character whereas if you were around friends you might drop the F Bomb on occasions.
I always used to laugh when I would see my mother interacting with her uncle. We would be on holiday with other relatives, cousins, aunts, uncles etc and it was fairly relaxed shall we say. However when my mother's uncle would turn up every year for the afternoon, everyone seemed to be on their best behaviour. It amused me at the time but now I realise that they were just modifying their behaviour for this particular occasion and their comfort zone around their uncle was a little bit smaller than normal.
I'm sure if Queen Elizabeth turned up at your place your would act very differently than if your mate showed up for a beer and to watch the big game.
Have a look at this clip in which we see how the Lionel Logue's wife acts when she finds out that Queen Elizabeth The Queen Mother is having a cup of tea in her dining room.
See, Mrs. Logue modified her behaviour to accommodate a very important visitor in her house. Of course after she had gotten over the shock.
To answer the question, yes it is OK to act differently around different people. It is called being a decent person and I am sure that if you are reading this blog then you are definitely a decent person as am I.