How scared should I be about DPS?

[winsock]

How stressed should I be about putting out top DPS as a healer?

At the end of the day, healer DPS is mostly a participation issue. There may be higher requirements if you want to join specific groups, but they'll let you know what those requirements are.

You shouldn't feel stressed at all about dpsing if you need to cast your strongest heals back to back to keep people alive.

You should feel stressed if you're casting nothing, spamming your weakest heals even though you don't need to save mp, or spamming heals on targets that don't need healing. Tanks and dps would face similar criticism if they were to sit idle, not use appropriate skills, or spam skills that had no value.