I have just looked over the code (this one, right?) and it seems to me that a better approach can be used to check for separators.

Currently you check at every character for the two possibilities (single or multi-byte separator):

if (c == csv->sep_char || is_SEPX (c)) {
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A better way would be to consider the multi-byte separator as a single-byte separator plus a tail:

/* somewhere on the object constructor */
csv->sep_tail_len = sep_len - 1;
csv->sep_tail = sep + 1;
csv->sep_char = *sep;
...

/* then, on the parser */
if (c == csv->sep_char) {
    if (!csv->sep_tail_len ||
        ((csv->size - csv->used >= csv->sep_tail_len) &&
         !memcmp(csv->bptr + csv->used, csv->sep_tail, csv->sep_tail_l
+en))) {
        /* you have a separator! */
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I think that would minimize the impact of supporting the extra multi-byte checks on the common single-byte separator case.