A part of constant-time coding is to avoid branches based on secret data, thus branch-free programming techniques apply. However, there is more to it; for instance, you must also avoid any memory access whose address depends on secret data (otherwise, the secret could leak through observation of the cache status).

On the other hand, branches that do not depend on secret data are OK in constant-time code. Typically, when you process a chunk of data, the chunk length is not secret, and there will be a loop whose exit condition really is a conditional jump that depends on the length.