Henry Mahan several years ago preached several messages in my area to a congregation of free willer's that believed in crosses and altars and Jesus pictures on the walls. They had just finished singing the song "on a hill far away stood a old rugged cross, I will cling to the old rugged cross". Henry got in the pulpit and said, If you cling to a cross you will go to hell. Next evening Henry made the statement, coming to a altar is not coming to Christ. The small church and it's pastor received with joy the message of Christ while the free will visitors went away in a huff saying, one night he threw out the cross and the next night he kicked out the altar. If a man has Christ in his heart it will manifest itself to the world, no need of cross lapels to make a statement.
I understand to a point where he is coming from - but I disagree with him.
Just because I cling to the cross, does not mean I am going to Hell.
Of course walking to the altar does not make you a Christian, anymore than walking into a garage makes you a car. But if you have a car with a problem - you go to the garage to seek answers and to get your car fixed. Sure, you can read a Chilton's auto repair manual - but it doesn't mean that you will be able to fix your auto.
But coming to the altar, you are saying, my life needs affixing - what needs to be done.
If I see a man wearing a crucifix, I would assume he is Catholic. If I see a man wearing (just) a cross- I would have an icebreaker to talk to him about the Lord.
So Friend of God - I would assume that man who told you the cross is offensive is only parroting what someone else said. And Wiman was correct in what he said about the true meaning of the cross.
I say, go ahead and wear it, and use it an opportunity to witness.
Lord Bless you.