Mixing Metals

No, absolutely not!

I prefer silver hardware and wear silver jewelry, but, my sunglasses have notable gold accents. I wanted silver accents but this style didn't come with silver accents. I used to wear a watch with mixed metals...stainless with yellow gold, which addressed this mixed metal concern nicely, although I no longer wear it.

Wear what you want and enjoy!!!
 
I'm a great one for mixing. The Europeans mix things up a lot too. I even mix silver and gold -- a silver Tiffany tank watch with black strap, with a gold Pomellato ring. Looks tres cool.
 
I think it is fine to mix. I usually wear silver jewelry and right now I am carrying my LMM in chocolate with gold hardware. I think it is fine. I don't think the hardware on your bag has to match your other metals.