Share /home and /var between two distros (Trisquel and Debian).

I can only tell you about /home, know nothing about /var.
It's possible, but it can cause some unpleasant effects in practice, mainly if you use same programs but different versions on your distros.

But if you make sure all versions are pretty equal (especially gnome or your DE) then this should be possible.

Technical this is possible but not really advisable.
Applications store their configuration stuff inside hidden files and directories.
They might interfere e.g. if you use different versions of the same tool in Debian and Trisquel.

No idea about /var.

As long as you don't use the same user name then sharing /home is fine.
If you have folders with stuff you want to access from both, then one possible solution is to make a folder at the root of /home and put them in there, then make it readable by all. You can then symlink that folder into appropriate home folders.
So /home would then look something like...

/home/account1
/home/account2
/home/stuff

Then in a terminal, something like 'ln -s /home/stuff/Music/* /home/account1/Music'

This a crude solution and issues arise quite quickly. But solutions based on the above and tuned accordingly are fairly easy to arrive at.