A good place to start when answering this question is the story of Moses and the 10 Commandments. One of the longest commandments given was about “idol worship,” and I think it’s relevant here.
You shall not make for yourself a graven image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth; you shall not bow down to them or serve them; for I the Lord your God am a jealous God, visiting the iniquity of the fathers upon the children to the third and the fourth generation of those who hate me, but showing steadfast love to thousands of those who love me and keep my commandments. -Exodus 20:4-6
This commandment is a reflection of God wanting His chosen people to completely separate themselves from anything that might make them appear to be part of the status quo, which was idol worship.
So, in a present culture where people don’t worship idols like before is it ok to wear a Crucifix? I would argue yes depending on your intent. If you are wearing a cross with Jesus on it to remind yourself that your salvation was bought and paid for by Christ’s sacrifice, ok. If you are wearing a cross to celebrate Christ’s resurrection, dope! I can dig it.
But….. And this is a big but. If you are wearing a cross because you think it in someway offers spiritual reward or protection, that’s where you can mess up. And now you are at risk for engaging in idol worship. So full stop and reprioritize.
What about angels?
This is a bit tricky, and I’m really not sure. God directed Moses to make replicas of cherubim for the Ark of the Covenant, so obviously creating images of angels isn’t always bad. Therefore, I’ll defer to the same rule as the cross.
What is your intent? Are wearing an angel around your neck as a reminder of God’s protection or are you seeking some favor from God. If it’s the latter, then you may want to rethink that.