No offense at all, it is an excellent question. My parents had a very flat accent and were considered 'posh' here in my mountains. As a kid, I loved to pick up the local accent, expression and words- but soon learnt that they were not welcome at home. Nothing to do with 'not being myself' at all- just accepting that some situations required different types of speech, and behaviour in general.
And then in the UK I lived and worked in London with people who had RP- and adopted same naturally (although my 'haitches' did let me down somewhat- which they all found funny). Then we moved to the Potteries, and in my new job all the staff, both white collar and shop-floor, had a strong Staffs accent- even my boss the MD- and I soon picked up the local accent at work and expressions. I have a very good ear for languages, and loved it. But back home with OH, family and friends, RP took over again. Then we moved to Leics, and same thing happened. I then went to Uni to become a Mod Langs teacher- and it was clear that to teach I had to use standard French (had to change the way I count, and many words too) and accent. An English teacher here, from, say, North Yorkshire, would do the same, quite naturally. But when we visited my parents, friends and family here, i switched back. Same me, same person- but it is just natural to do so.
In the UK, and here, we have a friends and family from vastly different background- I am no chameleon, but it is natural to adjust a little, at times a bit more. They have hugely different political views and life experiences too- which can be hard at times, but makes life so so interesting.