I'll start by saying, yes, you technically can attach them together. Just that it takes WAY too much effort, and a very very specific camera angle/distance to accomplish it. What's more, is I only managed to do so by dragging Blue on top of Pink.

Whether this is relevant, here's the full story:
These were part of a build I was modifying (as the AutoCredit indicates). To make matters less complex for this bug report. I isolated that away from that build (deleted those parts) since the rest of it didn't matter as this problem persisted either way.

These specific parts were originally obtained from existing pieces of that build which I copied, modified, rotated, resized (via Part Settings), and assembled -- these, when connected, would become the 'Thumb' that I added (as seen in 'JATO Betsy' build). The original parts, as with that entire build by Suubk27, were scaled to 0.1,0.1,0.1, however, trying to assemble them at THAT size was just as difficult (if not more, since snap points don't scale down unfortunately). As such, I scaled these back to 1,1,1 to make it easier.

However, it seems it went from 'a real pain in the ass' to 'pretty much impossible' when I imparted a little more rotation on the pieces (multi-selected, then rotated them as if one piece), as before then it was hard but not this difficult.

The interesting thing to point out is that Pink and Blue are the same basically (if not completely). Same length and same mating surface LxW, with identical rotations. Yet trying to connect Pink to Blue, or Blue to Pink -- with, or without the cone -- causes ALL MANNER of mayhem (see: frustration). This more or less goes the same for trying to connect that Orange one to the right, to the bottom of Pink (where it's meant to be connected).

After literally 45m to an hour, I finally managed to get them all back together, after which some kind mystical force was thankfully on my side because I had to then re-scale them back down to 0.1, but somehow I managed that in a quarter of that time!