There's a difference between being a tertiary technical problem solver and a rotational generic customer support person. I wouldn't quit immediately, but I'd start looking seriously for other companies. Why? Because I've done it. It's not something I'm suited for, and it's a dumb thing to expect me to be good at. I can respond to people if it's a fixed set and small set of them, on my team, about technical things. That's all he communication I can be good at, while doing engineering work. Otherwise it burns me out and makes me depressed.

I also make this very clear to my boss. "If you want someone on customer support, you want someone else instead of me."