I take a look at my match history each weekend. GUDecks gives you a nice/quick summary of the total number of relics in each deck. 2 weeks ago I was routinely seeing 3-4 relics per deck (also faced a lot of war). This week, my matchups were more varied and relics were like 1-2. Hard to make adjustments on the fly due to such small sample size, but the rest of my games after making the change were the same thing: few relics.

Also, it's not just "do they have any relics". It's how many and how important they are. I swapped in Bronze Servant originally because I was facing zombie death and war. It was marginally beneficial against other decks, too. Knocking out an enduring shield or necroscepter is a huge advantage. Knocking off 2 durability from Faeflame not so much.