It's not a legal incompatibility; FreeBSD has never shipped modified GPL software anyway to my knowledge (beyond things like patches to cleanly-separated ports that can be distributed independently under the GPL).
It's a philosophy thing. The new provisions in the GPLv3 (principly the counter-tivoization requirements which prevent shipping integrated devices without reprogrammability) are seen as unacceptable to the FreeBSD team. So they simply ruled against the license, which means that recent versions of gcc are unusable and they need to look elsewhere for a modern compiler.
That's the official answer. The cynical answer is that they've always hated the FSF and their dependence on GNU software, and are finally jumping ship now that there's a non-copyleft compiler available for them to use.
They wouldn't. Most situations where GPL exclusions are enforced are still willing to include a modern gcc toolchain.
But still, it's FreeBSD's distro, and they get to write the rules. And clang is a modern, attractive compiler. The feud may be dumb but the choice isn't.
If you were the only one in possession of oxygen I would buy it from you, but that would not imply that I had no problems with the idea of buying oxygen.
Also, the difference between GPL2 and GPL3 is large enough for many BSD backers to be of concern (the anti-Tivoisation clauses mean that one cannot close down firmware compiled with a GPL3'd version of gcc if it contains even the tiniest part of libc. Possibly, even using some of its macros in your code would be enough to require you to make your software GPL3. We won't know until this has been to court, but why take the risk?
Apple doesn't want to use GPLv3 because of the patent clause.