Why one term is acceptable over another could be because one is more of an official job specialty (infantryman), while another is merely a role within a fireteam.
That doesn’t seem to be the case. They are separate MOSs (military occupational specialties). A rifleman is MOS 311, while an infantry assault marine (nee infantry assaultman) is MOS 351.
Cool.navy.mil/usmc appears to have the answer. Riflemen:
employ the M16A2 service rifle, the M203 grenade launcher and the squad automatic weapon (SAW). Riflemen are the primary scouts, assault troops, and close combat forces available to the MAGTF. They are the foundation of the Marine infantry organization, and as such are the nucleus of the fire team in the rifle squad, the scout team in the LAR squad, scout-snipers in the infantry battalion, and reconnaissance or assault team in the reconnaissance units. Noncommissioned officers are assigned as fire team leaders, scout team leaders, rifle squad leaders, or rifle platoon guides.
While an infantry assaultman:
employs rockets, the Anti-Personnel Obstacle Breaching System (APOBS), and demolitions. Assaultmen provide rocket fire against fortified positions in support of the rifle squads, platoons, and companies within the infantry battalion. Additionally, Assaultmen employ APOBS, demolitions, and breaching/infiltration techniques to facilitate infantry maneuver in the offense, and demolitions and expedient counter mobility measures in the defense. Assaultmen are found in the assault sections of weapons platoons of the infantry rifle companies. Noncommissioned Officers are assigned as gunners, team, squad, and section leaders.
So it seems that a rifleman is the basic infantry soldier (committing a terrible faux pas there by calling a marine a soldier), while an infantry assault marine is more like a combat engineer and heavy weapons specialist.
The Navy is also considering altering some of the titles of their ratings (job specialties) and ranks.
The USMC is, of course, part of the Navy. It’s all part of the same bureaucratic exercise.
I can’t understand why anyone is upset by perfectly ordinary words, correctly applied and without malice aforethought.
I think upset is the wrong word. It’s just that people recognize that the use of gendered language subtly and insidiously perpetuates unconscious discrimination and bias. The problem is especially troublesome in job titles, where there is a direct link to who is hired for a particular position.