According to the POSIX specification:
The system may provide non-standard extensions. These are features not
required by POSIX.1-2008 and may include, but are not limited to:
- Non-conforming file systems (for example, legacy file systems for which _POSIX_NO_TRUNC is false, case-insensitive file systems, or network file systems)
So it looks like case sensitivity is the norm, but it is possible to support a non-compliant (case-insensitive) file system and still call your product UNIX as long as it can also support case-sensitive file systems.
Actually, see this part of the specification:
Two proposals were entertained regarding case folding in filenames:
- Remove all wording that previously permitted case folding.
Case folding is inconsistent with the portable filename character set and filename definitions (all bytes except <slash> and null). No known implementations allowing all bytes except <slash> and null also do case folding.
- Change "though this practice is not recommended:" to "although this practice is strongly discouraged."
If case folding must be included in POSIX.1, the wording should be stronger to discourage the practice.
The consensus selected the first proposal. Otherwise, a conforming application would have to assume that case folding would occur when it was not wanted, but that it would not occur when it was wanted.
So it looks like is purposely left ambiguous - it is neither explicitly permitted nor forbidden.