Well, you MUST keep them separate obviously, but separate sets of contacts is separate. There are rules about the wiring, i.e. all wire insulation in a common space must be rated for the highest voltage in the space, but that's rarely an issue.
There are code issues about separation and isolation with regards to medical equipment, but "low voltage" in that realm is 10V or less.
There are UL listing issues with regards to "limited energy circuits", wherein the 24V may need to be sourced from a "Class II transformer", meaning no more than 100VA available on the circuit in order to avoid having to have the devices it feed be UL listed. But I still don't think that precludes connecting the circuits on the same relay.
So in a word, no.
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