Welcome to the forums!
I just recently reworked my whole template and hence bumped against this same question, and after some head scratching eventually got it working pretty much similarly to Reaper, although it is a lot hackier to setup in Renoise. You need at least 4 outputs to do this, so if your audio interface has only 2, you need to use virtual outputs (at least VoiceMeeter works perfectly for this).
You can do this by routing your whole mix through 2 send tracks and configuring your track output routing in this way:
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First, set your master track’s output to your audio interfaces outputs 3&4 (or basically any other output than 1&2, if you are actually monitoring through 1&2).
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After this create two new send tracks. The first one functions basically as your mixbus, so you need figure out a routing that sends your whole mix to it. The second one functions as you “listen/monitorFX” track.
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At the end of your “mixbus” FX chain, put a send device that sends your whole mix to the “listen/monitorFX” track. Set the send device to “keep source” mode.
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Route the second “listen/monitorFX” track to your audio interfaces outputs 1&2.
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Insert any monitoring FX to the “listen/monitorFX” track and you will be listening through them, but they won’t be applied to your renders.
This method has some minor quirks you might run into and it can totally break your master level meter and clip indicator (to counter this, you can put a separate level metering plugin on your Monitor FX chain). But although hacky, it works essentially the same way that Reaper’s monitoring FX work. With this method you don’t necessarily need to route to any other applications, and this also doesn’t bring any major increase of latency. Now AFAIK you can’t save this setup to any user preferences, but you can put this into your template and also save any of your commonly used FX chains separately. There’s also a tool for managing multiple templates if that would make your life easier (it’s called “quick template” if I remember correctly).
As a bonus tip, if you have a decent measuring microphone and know how to operate RoomEqWizard, you can actually use Renoise’s convolver device as a perfectly functional room correction eq. So no need for room correction VSTs with Renoise. I have it wrapped up in a doofer, coupled with a tilt eq (for “house curve” adjustments) and a gainer device for gain compensation. This setup allows me to just toggle it on/off with a single button if I need to switch to headphones, and it’s perfectly gain compensated and all. Was a really nice find when I recently figured it out.
Cheers! I hope this helps!