I'm going to tackle this subject in terms of AAVE and Gullah dialects given that Mark Twain has come up in this thread. Some people find phonetically spelled renditions of AAVE and Gullah are offensive and some people find that they are respectful. It honestly depends on the time period, the character, the rest of the characters in the story, and the framing.
For instance, if you were to write a black character with a phonetically spelled accent, whether or not that's going to upset people is generally going to lie in how respectful you are of that character outside of their accent. If they're a token character, and the rest of your characters are white without phonetically spoken accents (effectively marking your POC exclusively through the way that they speak and "otherizing" them), and negative stereotypes are present in your presentation of the character, it's going to be pretty much flat out racist. If your only motivation for phonetically spelling out an AAVE or Gullah accent is to differentiate them from your white characters in an ignorant manner, you're doing something wrong.
However, there are times, such as in The Adventures of Huckleberry Finn, where I feel like it would almost be more disrespectful not to include how that character speaks. Additionally, when you have more than just one representation of POC and they're treated like human beings instead of brownie points for diversity or lazy tropes or you have done extensive research into the culture, I feel like that's a different matter. It really all lies in how respectful you are of the character and the culture they come from. I am, however, white, and there's a good chance I don't know what I'm talking about.
There's another discussion to be had about the various different English accents and the political connotation behind spelling them phonetically. Classism is much more pronounced in England than it is in America, and accents are linked very tightly with that. Phonetically spelling different English accents could be a very easy cheat to mark where someone is from or to mark their class, but you walk a fine line with the latter option - it comes down, again, to your respectfulness to that character and their narrative and the culture they come from.
So, when it comes to the politics of it, it really does lie in the writer. If the writer is bigoted (even subconsciously or accidentally bigoted), it's going to come across as bigoted. If the writer is spelling it phonetically because they're trying to alienate that accent as "weird", it's going to come across that way. It depends entirely on the writer and the context and the framing of the novel.
Now that I've got that out of my system, there's an entirely different discussion to be had with whether or not it should be used for practical purposes:
1. You risk slowing the pace of your story.
2. Phonetically spelled accents are not translatable to other languages.
3. It may drive readers away; many people set a book down if a phonetically spelled accent is too frequently used/overwhelming.
My advice to you is to consider the practical arguments and the political arguments. Talk to people with Jamaican accents - this is the internet, you can find anyone anywhere - and ask how they feel about what it is that you have written. Consider how often this character shows up. Think very critically about why you want to write the accent phonetically, how you treat the character, and how you treat that character's culture.
