For common 4k long GOP codecs, non-rendered playback with no effects is typically a CPU-bound (or Quick Sync) task. For low-compression codecs ProRes, etc, it can be I/O bound. If effects are used it can be GPU-bound.
I've only briefly tested RED RAW, and don't remember the results. However since it's having to debayer each frame, this would seem to be either CPU or GPU centric. Since the Mac Mini doesn't have a discrete GPU that might be the issue -- but I don't know if FCPX does GPU debayering for RED RAW. I think Resolve does.
Depending on what RED compression factor is used, the I/O load could also be fairly high, esp. for multicam. RED 5k 2:1 is 68 MB/sec per stream:
https://www.red.com/recording-time
When the iMac Pro was released there were lots of demos showing timeline smoothness on RED footage, without proxies or optimized media. So it is possible but maybe not with an i3 Mac Mini. Re whether an i5 or i7 Mac Mini with an eGPU could do that, I tend to doubt it -- at least on current software.
Max Yuryev tested 4.5k RED RAW eGPU improvement on various MacBook Pros, and there wasn't a huge improvement:
You can create optimized or proxy media but this locks in the currently-selected RAW parameters. That would probably give decent performance on a Mac Mini, but if those are changed the proxies/optimized media would require rebuilding.
A six-core top-spec Mac Mini with a Vega64 in an eGPU might do OK, but it's nearly as expensive as the entry-level iMac Pro when on sale. The 8-core Vega56 iMac Pro is sometimes available for $3999 from Micro Center and other places:
https://www.macrumors.com/2018/01/29/imac-pro-micro-center-1000-off-deal/
If you want a sanity check on whether FCPX is handling the codec poorly for that hardware, you can try Resolve. The latest versions are pretty fast. If you get an eGPU to test, I'd definitely suggest testing Resolve, since (in general) it heavily uses the GPU. However I don't know if the free version handles RED -- Blackmagic has increasingly been withholding features from the free version.
Info on handling RED footage with various NLEs, inc'l FCPX:
https://blog.frame.io/2018/04/30/red-workflows/
Apple info on handling RED footage in FCPX:
https://support.apple.com/kb/PH12755?locale=en_US