Once I complete certain missions in the Far Cry 3 Story line, can I revisit old islands?

Short version:
Yes, you can revisit the islands and you will not miss anything important.

Long version:
There will be certain places (caves, buildings) that are only accessible in missions while you are doing the specific mission. Once the mission is over, you might not be able to access the specific place anymore.

This will include items that you can gather in specific locations. If you want to gather the maximum amount of items, it is recommended that you pickup everything that is not accessible as an open space (i.e. inside caves, houses, fenced in areas) during the mission. Everything that is visible as loot on the large map should be accessible anytime.

In other words:

Once you finished all missions, you can fast-travel to both islands and access all relics and loot that is on the main map visible by buying the maps from the shop. However, if a mission brought you inside a house where you could pickup something, it might be unavailable once that mission is finished. Those items normally do not show up on the large world map however.

The very first relic is in

the cave right next to Dr Earnhardt's house, apparently.

After a certain point in the story you can't get back in there so pick it up early on.

It's the only thing I haven't done/collected in the entire single player game and unless a patch is released at some point that allows you back into the cave, my progress rating will be stuck at 99%...

Yes, apart from the first relic I would agree, but be sure to regularly save your game (don't rely on autosaves). I have done all the story quests, and they have disappeared off the map, but i have lost credits for 2 of them- the handbook says i have 2 more to do. Likewise, I got the xbox achievement for all the memory cards, next time I played i had 15? Same with some of the relics- I had to get some twice. I'm stuck now at 99% completion, and can't get to 100% because the Story Quests are done, off the maps, but not "credited". It doesn't really matter, but to get so close and be blocked by a glitch... At least the relic/ memory card issue re-showed their locations on the map, but the story quests did not- even after this latest patch release, though at least i got relic 1 that way, better if they had opened the cave up, but there you go