A chameleon of accents

It was during one of my first classes for my bachelor English, I think it must have been some Linguistics course, that I realised that not everybody speaks the same English. Up until that moment, British English and American English and Australian English sounded perfectly similar to me (I did like the people in Australian series better, but that may have been because the Australians simply make better youth tv series). This was the same as listening to my grandfather speak to my mother, he with a strong local accent, she answering in standard Dutch: I could understand both of them, so I didn't notice that they were speaking different accents.
After thinking about this for a while, I have decided that this was not weird. It may have been weird because I was studying English, and thus must have had some under laying affinity with the language, and thus may have noticed these differences before, but as I was mainly studying English for the written variety (literature, perhaps writing some things myself), this wasn't really an issue.
But for me, accents have never really been an issue. My mother never tires of telling how I, after we'd been in France for a couple of days, perfectly adapted to the French accent and would call "mama!" in the French rather than the Dutch way (there is a strong difference between these two), copying the French kids around me. I have also spoken with an Amsterdam accent for a while, which may have been influenced by the tv programmes I watched. Then, when I started getting friends in the south of the Netherlands, my accent shifted to their pronunciation, sometimes to the confusion of my northerly friends.
It took quite a long while to fix on a 'proper' accent for my English studies (yes, we get proficiency in the language as well), perhaps because of all the mixed influences I was getting. I have been called Mid-Atlantic by some, which is not really a compliment. But finally, I picked British English, and passed my speaking courses with this. However, after only a week in America, people started to ask me where I lived or studied, as my accent was so genuine (I have since found out that Americans will say that someones English is 'great' when they can utter simple sentences, but I have the feeling that this went a bit further than that). I also noticed in myself that I started pronouncing things in an American way; rhotic (that means, pronouncing the 'r' in certain locations in words, Americans do this, most British don't) and generally rolling the words around in my mouth more, the way Americans do.
I think this is simply an adaptive strategy. When I talked in British English, I sometimes had to repeat myself as others did not immediately understand me. When I went with the American accent, it was easier to make myself understood, and it was also easier to deal with things without getting the added 'she's a foreigner!' bit. Same goes for my Dutch accents; it is adaptive, but also a way of blending in. When in the south of the country, if you speak in a strong northern accent, people will look at you in a funny way, and you immediately feel like you don't belong.
I have no idea why I do this (it is clearly not a conscious effort on my part, even more, I was trying to maintain my British accent in America and failed miserably): it is an automatic thing. When talking to an Indian shopkeeper in America, I almost replied to him with an Indian accent, but caught myself just in time (I was afraid he may have thought that I was making fun of him or something). It comes in handy, usually, as like I said people will take less notice and you will blend in. But it does puzzle me, and sometimes worries me a bit. The way you speak shows where you're from, your background, your culture, your roots. If I will just adapt to whatever location I find myself in, people will never go "ah, but she's from the north! clearly!" when I open my mouth. This may be a good thing, in some instances, but on the whole I would like it if my accents would be a bit more stable, and I would be a little bit less of a copycat.