Out of curiosity, how would someone with good customer skills handle this situation?
Obviously, some companies make a conscious decision not to support all browsers, so there might be no way around it in that case.
But as an engineer, are you even remotely interested in learning good customer service skills... or making sure the site doesn't come crashing down in an hour?
To answer the first half of your question: as an engineer myself, I am personally very invested in good customer service skills. Admittedly, doing a startup (vs. being part of a much larger organization) probably drives my customer interest quite a bit. However, even from an engineering perspective the customer interaction has definitely helped to focus my work on solving real (often recurring) customer pain points and requests, and communicating those back to the customer in a way they understand.
anybody out there with similar experiences as an engineer doing both customer support and development?
This specific case is my day job. We're still startupy-ish, but a little more established (you've definitely heard of us). We have a support team and all that, and the engineers are working on new features and scaling more-so than bug fixes.
I (of course) am working on my own thing and handle 99% of the customer service on it - not only because I want my customers to be happy, but just like you said, I want to work on what really pains my customers.