When I started shooting IPSC rifle last summer, I asked about this, since I'd been shooting CQB with a chest rig, and was told that chest rigs were not allowed per Rule 5.3.1-Appropriate Dress:
The use of camouflage or other similar types of military or police garments other than by competitors who are law enforcement or military personnel is discouraged. The Match Director will be the final authority in respect of what garments must not be worn by competitors.
So, I bought the Bladetech pouches and set up a belt for IPSC. When I got to the matches, almost everybody was set up similarly, although I do remember one guy with a chest rig. In that case, the MD didn't seem to care, and neither did anybody else. This was a Level 1 match, so it was pretty relaxed. If it were L3, it would be a lot stricter.
So, technically, according to the rules, if you show up with a chest rig, and the MD considers it to be a "military garment", then it may be a no-go. In any event, it is "discouraged" (at least it was for me).