I’m from New York and I definately pronounce “writer” and “rider” differently. The first syllable of “rider” is slightly more ephasized, and the “i” sound a little longer. (I’m no linguist, that’s the best I can describe it.)
Is this across the board? How do these pairs turn out in your pronunciation?
*hole / hull
rut / rote
cup / cope
sun / sewn
rust / roast*
…
FTR, colt and cult are different for me. I’d describe my “o” in “colt” to be the “o” in “Coke”. For me, the “u” in “cult” is the same “u” as in “munch”.
Same with me, bordelond.
From Philadelphia, but from what I have read in linguistics books, what I am about to say is fairly widespread in the US. First the consonant in the middle is neither a “d” nor a “t”, but what linguists call a domal tap. The tip of the tongue taps (for me, it grazes) the roof of the mouth (dome). I have heard the same sound when Englishmen (more precisely, Londoners) say “Sorry”. Now the vowel. Normally in English we neither make nor hear any distinctions in vowel length. It is almost impossible for me to distinguish “Stadt” from “Staat” in German unless they are highly exaggerated. But I easily distinguish “rider” from “writer” and “ladder” from “latter” by vowel length alone, even when they are spoken in isolation. And the latter two are a better example, since there is no “w” to confuse the issue.
The best explanation for this is that back in the days that those intervocalic consonants were pronounced, there was a slight, but non-significant (also insignificant) lengthening before the “d” that was purely phonetic. But when the “d” and “t” fell together, these changes got to be significant (in both senses) and have remained so, at least in many dialects.
I’m Northern Californian, but I have often been accused of speaking with an accent (from somewhere other than this place). I wouldn’t say my accent is completely out of place for my region, but it isn’t typical either. Oddly, when I was making phone calls to Florida nobody there could understand a single word I said.
I almost never pronounce a “T” in the middle of a word. If you ask me where I’m from, I’ll say “Sacramenno” or “Sanna Cruz”. I’ll say “rider” and “writer” the same, and a mountain is a “moun’in” to me.
But then I generally tend to talk fast and slur a lot. I usually say “prolly” for “probably” and I’ve been known to convey whole sentences in a coupla syllables.
Mississippian here. I pronounce “writer” RYE-Tur, with the domal tap Hari Seldon describes in the middle.
“Rider” is pronounced RYE-dur, with no domal tap.
Those pairs are all different to me. “Colt” and “cult” are different, but very close. “Hole” and “hull” are the same. They’re different, but very close. The others are all significantly different.
What part of Michigan? The Detroit accent is much different from the rest of the state. I’ve lived in Detroit my whole life and never heard anyone pronounce “writer” and “rider” the same.
Coming from the land down under, many people say shore the same way as sure, caught the same way as court and car is pronounced kah.
However, we say rye-tuh and rye-duh
I think a lot of Americans think they’re pronouncing the T in “writer” as a T, but actually aren’t (and are pronouncing it closer to a D).
If I heard an American pronouncing the T, it would sound a little odd to me. It’s one of the most distinctive elements of the English accent. (And it’s one of the things that made Marilyn Monroe’s diction so absurd sometimes.)
Thanks for all the interesting posts and for the welcome. 
I haven’t read all the posts yet but someone mentioned T becoming a D in the middle of a word… It’s been a while since my last linguistics course, but this is called Voice Assimilation, isn’t it? It happens when a T is between two voiced sounds (two vowels, voiced) and it transforms the voiceless T to its voiced counterpart, the D.
Which is why I said:
Or to put it another way: I met a girl from Savannah, Georgia. I told her I liked her accent. She said, “Ah don’t hayav an accent. Y’alls got thuh accent!”
I’m from Clio (between Flint and Saginaw). I guess I never noticed that Detroit had a separate accent…
BTW, someone mentioned pronouncing “mountain” “moun’in”. I’d say I’m probably closer to “mou’un”, except when I’m in Voiceover mode (in which case it becomes “moun-tun”).