I am from the New England area, which is notorious for bad accents. Mine is a little worse than others, though. I am often mistaken by people I don't know well as being a Brooklyn or Long Island native, which I am not.
Also, I can do a pretty good British accent as well as speak in a few other languages, as well as read in many more. I too adopt the accents and sometimes languages of people I am speaking with.
For example, if someone I talk to natively speaks Spanish, I will adopt a Spanish accent while talking to them, even if we are both speaking English. I could probably be described as multidialectal and multilingual, but when I'm in regular conversation with relatives, I switch around a lot, but usually sound like I belong in a tri state area gang.
I don't live in Boston or Providence, by the way. But, I spend a lot of time in those cities so my accent is somewhat close to that and very thick, but a little stronger and leaning more towards a NYC accent, although I can only dream of going there.
I have been described as monotone too. In fact, when I was evaluated by an institution, they described it as "limited tonal fluctuation." Curse them, haha. If only they knew I can change my voice at will. Oh, well. It's my secret.
Personally, I don't think accent has much to do with autism.
Gosh, I am like this as well! I adopt all sorts of accents and mannerisms. Sometimes people are flattered by it, other times I can tell it makes them feel awkward. I do it unconsciously though.
My voice is monotone and nasal. I have been told by someone I was deeply in love with that it sounded very nerdy and that it wasn't attractive.