I’m running a Mid-2009 MacBookPro 15", processor 2,66GHz Intel Core 2 Duo, Memory 8GB 1067 MHz DDR3, Graphics NVIDIA GeForce 9400M 256MB with OS X El Capitan 10.11.6. My machine is fairly slow, being 8 years old.
Should I be running the 32-bit or the 64-bit version of Renoise on it? Which one is less CPU intensive?
Without a doubt the 64 bit version as the native instruction set is 64 bit for the processor you mention. 64 bit means that more data can be moved around faster in larger chunks resulting in better throughout in general. This also means it can take advantage of larger RAM or memory sizes and will be best for large Kontakt like libraries. 32 bit for Windows now runs on Wow64 or Windows on Windows technology which runs 32 bit applications in a created runtine subsystem that runs via pipelining system dlls and marshalling code via the runtime, this will result in a little though negligible overhead for light tasks though for more intensive data requirements the stress will show. Being multi core means that Renoise will be able to use cores for processing increasing efficiency.
if you can, run 64bit progs on 64bit OS on 64bit CPU.
just because the number is double, won’t mean it will be slower on weaker CPUs. The contrary will be the case. 64bit is an architecture capable of more performance for many tasks, running 32bit progs on a 64bit cpu is like using an artificial speed limitation.
Use the 64bit version. Try to use 64 bit plugins only and dont use renoise’s bit bridge or sandbox, a since it is a real performance hog. Keep on eye on highly optimizing vst vendors like native instruments. Often older versions of plugins perform much faster, and yes, you can create a charts hit even with old plugins. And today the hardcore programmers die out (inline assembler!!) and instead they use ugly, slow high level languages running in vms 
Buy a sdd, disable spotlight for some dirs, that can speed up your Mac. Uninstall anti-virus.