It was largely inconsistent for the most part. For the D-Day invasion, all American units used some system of white bars to identify the officers and NCOs. Officers had a single white vertical bar and NCOs had a horizontal one, although this varied from officer to officer. Some officers actually painted the rank on the front, but most removed it altogether to avoid getting shot by snipers.

Of course, SPR is a film, so take it all with a grain of salt; this criticism has been raised against the film before, I recall. Photographic evidence does show Ranger officers with white painted rank insignia on their helmets, and others show that some used black paint. (Ted Danson's character uses black painted insignia). Nevertheless I think the movie does take license by showing it to distinguish his rank in particular for the sake of filmmaking.

I've found some further evidence from the well-researched and cited Saving Private Ryan Online Encyclopedia about specific divisions and battalions having distinct rules. Summarized here:

29th Infantry Division: required on front

2nd and 5th Ranger battalions: orange diamond on back with number inside indicating battalion and white rank marker place in different positions around it

101st Airborne: used symbols from playing cards on the side and used a system of dashes to specify which battalion they’re from.

D day naval beach battalion was required to have a grey band around their helmet to distinguish them as navy personnel.

edit: formatting