Here's the thing. A cross is not a piece of jewelry or a necklace. It's a symbol of your Faith. It is an instrument that defeated death. It is more than mere decoration or a symbolism representing your "christianity".
Therefore, in my opinion, wearing anything alongside the cross (same chain) is wrong. Nothing is "equal" or compares to it.
If you wish to wear nationalistic jewelry (ie. Ukrainians wear the trizub - trident), I would wear it on a separate chain, hanging lower than the Cross.
To wear things around your neck along with a cross gives equality to them in ways. The cross is a symbol of faith, along with a reminder to people of their faith.
Also the conflict of interest. Consider as the symbol of faith, our god said "I am the way, I am the truth, I am the life, no one comes to the father but by me".... Then next to the cross is an ankh. Sort of makes it seem like a person isn't really serious about their faith.
Orthodox crosses are also often blessed, and this would seem like a huge conflict to an Orthodox Christian to wear something blessed to something that theologically is not Christian.