No, the Kemper does not provide the functions of a DI box as it outputs line level signal rather than low impedance mic-level signal. The latter would be required to a) feed a mic input on a mixer and b) drive long mic cable distances without degradation. So, you often still need a DI box unless you have a mixer input with built-in mic/line switching or pad functions (these are actually quite common on stageboxes that accompany digital desks, and highly useful).
You can use either active or passive DIs with the Kemper, just be aware of the pros and cons as outlined above. Radial make great examples of both. If I could carry only one it would be passive.
If it’s a mixer with a separate TRS Line input (common) you can connect straight to that from the Kemper’s output, with an XLR>TRS cable for example. This is great until you need to drive long cable runs through a multicore back to the desk. That said, the Kemper line output drivers are good. Chances are onstage though that you’ll only be given a wall box that feeds mic inputs on an in-house mixer. I’ve found that asking a hired-in engineer to start re-patching to line ins is asking for trouble, so I much prefer the idea of presenting a pair of D.I. outputs they can pick up.
What can catch people out is on the back of the Rack and Toaster, you have a ‘Direct Output’ but this is an unbalanced 1/4” TS jack, and its level varies depending on where you choose to feed it from in the signal path, but it will never be low impedance mic level or balanced as that is not its purpose.
I’m wondering if I confused things by putting “..(the Kemper in this case)...” ? I was referring to the Kemper being the source connected to the input of the active DI, not it being the active DI itself.
If this doesn’t clear things up still let me know and I’ll give it another crack.