Because we love Him, anything that is important to Him should be important to us.
The cross was prophesied in Psalms 22 and Isaiah 53. And Jesus' fulfillment changed everything forevermore.
And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all [things] he might have the preeminence.
For it pleased [the Father] that in him should all fulness dwell; And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, [I say], whether [they be] things in earth, or things in heaven. Colossians 1:15-20
It certainly is, to me.
Just as I show some degree of reverence for the printed Word of God . . . though I still mark the pages up etc.
And I don’t even begin to worship either a cross or a Bible.
I once did get close to idolatry of the Bible, but The Lord brought me up short about that.
Symbols can be useful. They can be hazardous. The attitude of the heart, imho, is crucial.
I prefer a kind of reverence for THE TRUTH OF THE CROSS . . . not per se any physical representation of it.
Though I would take care to protect a cross or treat it with respect OUT OF RESPECT FOR THE TRUTH OF THE ORIGINAL CROSS.
If I had to break up and burn a cross to feed a starving child a hot meal and warm them a bit, I would not hesitate more than a few seconds.