It’s not clear if you mean support for a fully POSIX/SUS3 compliant layer (which would need to include shell, utility applications, networking services, etc.) or just the C library portion. In either case, a better and more constrained target would be targeting support of the C11 standard library first.
The major assumption that the C11 library makes is the assumption that every process has access to some key/value store that maps string names to capabilities of block and stream I/O objects. How that fits or abstracts over the seL4 model of capabilities is something that would require a lot of though.
In the case of POSIX, which requires some sense of a ‘global’ scope within which processes operate, it may make sense to have a framework for constructing isolated container-like systems which offer a POSIX world to the processes within them wherein processes that are built entirely on the POSIX API are constrained to that world but processes or libraries also using the underlying seL4 API (such as those for networks or filesystems) have some means of communicating with traditional seL4 (non-POSIX) processes outside of the POSIX container.
It is clear, however, that providing compatibility for POSIX on top of seL4 would require a lot of design work and forethought and would require some well-defined and reusable systems for managing and partitioning network, file-system, and shared memory access (among other OS services). As such, there is a lot that needs to be done before we can start to piece together an abstraction that satisfies even a minimal subset of the POSIX specification.