I looked into getting an eGPU for a Macbook in 2013. Thunderbolt 2 has the bandwidth to make it possible, but it's not ideal and will cost performance.

More critically, at least in 2013, the docks you needed cost thousands of dollars—and made more sense to just get a separate desktop PC. I don't know if the situation has changed since then—there are more eGPUs out there but it's all for Thunderbolt 3. Thunderbolt 2 is more niche and thus may be more expensive.

It's possible to use at least some TB3 eGPUs with TB2 and adapters, it's not officially supported by Apple on macOS though. They are still insanely expensive in my opinion for what's basically a case, small PSU and PCI-E to TB3. The cheapest ones that can take most cards are around $300 and usually have some downside. I considered it for my Mac Mini but in the end it just made more sense to sell the Mini and buy a desktop PC with space for a real GPU, more storage, faster processor, etc. I mean my case, power supply and motherboard was less than the price of a Razer Core X...

Thunderbolt 2, if supported natively by the hardware and using an external monitor, might actually be enough in practice. I used to game on rMBP 2015 with a GTX 1080 in a TB2-connected eGPU and it didn't even saturate the link, so when I upgraded to an iMac with TB3 the performance was pretty much identical.

The rule of thumb is: use an external monitor and the highest resolution possible. Sending control commands one way consumes much less bandwidth if you don't need to send whole images back down the link, and the high resolution and quality is to make the GPU the bottleneck, not the TB2 link.

The other issue is drivers. Nvidia is definitely out since the drivers have not been updated in many years.

I found egpu.io to be a fairly reliable source. Check out their build section to see if anyone has successfully paired an eGPU with your Mac model.

I was able to get a ThunderBolt 2 Mac to work with a Razor Core + Vega 56 combo, but YMMV. Away from computer so don’t remember exact year for my MBP, circa 2015 maybe?

Do you intend to use the GPU for rendering with Cycles? This isn't possible with current versions of Blender on macOS as Nvidia has stopped development of the CUDA toolkit for macOS and Apple has deprecated the OpenCL compiler. Since Cycles doesn't yet support Metal you cannot use GPU rendering on macOS. It is planned though and there are improvements being made with the Cycles X project. It is possible to use other render engines that support Metal though.

I used to do a lot of Blender work on a 2013 macbook pro (up until last year or so). It's fine for modeling, but rendering is rather slow as the macbook thermal throttles when all its cores are being used.