This is probably a dumb question but I was wondering why accents seem to only or mostly vowel based?
For example we endlessly agrue over the way to pronounce Mary, Merry, Marry.
The variance seems to be always the vowels. Why can we agree that an “M” always makes the “mmm” sounds but we cannot/do not agree on the vowels sounds. What is it that is fundamentally different about vowels?
It’s also about which syllables you stress, but there are definitely differences in the consonants as well. Ask a Cockney to pronounce “brother”. And sometimes consonants are dropped altogether. But yes, vowels count for a lot in accent determination and you will often hear about vowel shifts as languages evolve.
Nothin’. There’s plenty of variance in consonants, as well. Say to an Englishman, “Y’know, it’s funny how butter and ladder have the same sound in the middle but are spelled differently,” and he’ll say, “Wot wot?” (Or perhaps, “Cheerio!” 
) /t/ and /d/ are two very different phonemes over there, whereas here in Chicagoland they’re interchangeable in the middle of words.
"R"s have a huge variance in the US, from over there in Boston where they’ve voted to eliminate them to Minnesota where they swallow them.
“ch” making the /k/ sound in Scottish accented English, of course, is a very different sound than mine.
I know there are more, but that should do for a start.
I knew someone would bring up the “R” sounds. I believe R can be construed as a vowel (cite lacking but I know I’ve seen it).
Those other examples are hard for me to comprehend. This is tantamount to saying that in schools, the students are shown a letter, like D and told it is a “tee”.
I consider that a mispronunciation (no matter how wide spread it is - and I don’t want to go down the nuclear-newcular snakepit).
Saying ax for ask and liberry for library are not accent differences.
For purposes of this discussion I’d like to keep it strictly American accent variants.
Well, I’m not sure what to tell you, then. I can assure you that the “budder” = “butter” variant is certainly widespread and old enough to be considered a trait of more than one regional dialect.
If you’re asking questions about accents (or dialects), then you don’t really get to decide what makes up an accent or dialect. Those are already defined terms within a specific field.