My experiences with color in-character is that the individual in question is skewing the perception of that character in the mind of the reader by use of their color choice. In this I mean that it has been largely stereotyped that your "red text" characters are your fiery spirits, evil doers, villains, crazies and the sort, whereas your greens are much more neutral, passive or calm - often akin to blue and so on for each. This has two effects on myself as a reader, both of which I am not fond of...
First, the issue I take the most problem with is that it just looks horrible to my perception. It is not pleasing to encounter and is often very jarring in contrast to what could be better done with more classical, proven tools of writing such as word choice, phrasing and utilizing of emphasis. Even changes such as bold or Italics (in particular underline or strike) can be too jarring if executed poorly, which they often are. A colored response tends toward the extremes in these regards, especially when mixed with default text - it just has the sensation of, at least for myself, being struck in the face by the text because it is very much the center of attention. I do not have the option as the reader to "not" view it until I get there; it is distracting.
The second issue I take with it is that it appears lazy, as many have said. This stems from more of a formatting issue and improper use of alternating speaking roles between characters, which if done in the same post can be made quite clear, even in its simplest of forms (the "said" archetype). If one is posting for many characters in different locations, why not employ a divider with a slightly larger font size denoting the character and location, then proceed from there effectively in-character after said transition? It appears smooth and allows the reader's train of though to reset, to become accustomed to the "new" information that is not (normally) directly linked to the previous? It runs along the lines of chapters in a book, in terms of concept - of which I am certain there is likely a word to describe it.
Building off the second issue of laziness, it gives a sensation that a character, even if absolutely not, is but a single note. "My character X is Y because his/her color is Z." Perhaps this is just my opinion alone, but it feels very stereotyped - that the character is bound to, rather than their words and deeds, their color. Again, readily rectified by superior word choice, phrasing and emphasis (like that of Italics and the sort).
Color does have its uses in roleplaying, some of which I am fond of - especially as a Game Master. I utilize it almost strictly for "set pieces" such as my account's profile information, but more so for something where it is most effective... statistics. In a very "crunchy" and mechanics heavy roleplay effective use of color by a Game Master can indicate the severity of statistics; the difference between 1/100 and 1/100. It does however, require discipline and elegance to employ correctly, or it comes off as breaking any semblance of immersion, which is essentially the lifeblood of roleplaying, which is even more vulnerable in any system that uses a lot of hard rules and numbers.
Admittedly, colored text and its users are not about to really go anywhere. They're not wrong, as it is by and large preference, but I further admit I do not take much interest in it and often utilize a policy of declining its use in any roleplay I run or participate in; no more different than how I avoid and tend to disapprove of character pictures of which are not original works - unique to that character - and or are not genre appropriate, such as anime pieces in a decidedly non-anime realism setting.
