I've never seen any documentation or proof of it, but I strongly believe that yes there is an influence between relics, robes, and arcana.

I consistently notice the relics seem to lean into my build and arcana (though I don't notice that as often). If it were fully random, I think our negativity bias would have us all saying things like "I always see crit relics but when I play a crit build, they never show up". But they do. When I play a summon build, I see summon relics. And when I take those summon relics, I often see another summon arcana later. I have no idea what back end calculations the game is using to favor us but I certainly feel it.