Out of Tune Effect

Does Renoise have any native effects that make noise go slightly in and out of tune?

I guess you mean the wet side of a chorus?

100% wet chorus without feedback is like vibrato. It will be weaker the slower the lfo freq is.

You could also play with pitch modulation on renoise instruments or pitch bend if you use vstis. This can detune on instrument playback level, not on effect level.

If you wish to long for that ultimate “detune anything to sound beautifully like digital metallic junk on demand” effect, try looking for “frequency shifter” vst effect plugins. Then automate the shift amount. No shift will sound normal, and the further you shift up or down the whackier detuned against itself the sound will become - frequency shifters shift low frequencies stronger than the high ones, that is why. This is different than pitch shifters which would keep the harmonic relationship and eat up your cpu. On sine waves freq shifters are boring, on sounds with harmonics - they are mayhem. Those are the bad boys. Renoise doesn’t have a frequency shifter.