Is accessing theme and using customizer GPL distribution?

In my understanding (and I’m not a lawyer, etc etc), this would not count as distribution.

I make this distinction mainly based on the fact that a separate GPL-flavoured license actually exists where this would count as distribution – the GNU Affero General Public License.

GitHub’s choosealicense.com states:

GNU AGPLv3 is distinguished from GNU GPLv3 in that hosted services
using the code are considered distribution and trigger the copyleft
requirements.

(http://choosealicense.com/licenses/agpl-3.0/)

Therefore, as long as you’re using the GPL and not AGPL, I believe what you’re doing wouldn’t count as distribution.

Remember though that once you sell your theme under the GPL, the buyer can do whatever they like with it – including posting the source code online for free.