I had never heard of this before I read this thread. I've thought about it off and on since then and have enjoyed the discussion. I don't think it belongs in the Antimustaschian category. The OP has decided what values/goals are important to them and it's cool that they have, not everybody does.
No need to feel any guilt-- you have spent your money on something that is important to you with low impact on others (ie you're not being cheap and you are cleaning up after yourself) and low impact on the environment( reusable chairs, tables, LOW PLAStTIC tableware and LOW PACKAGING food in resuable containers).
Consider the analogy of running in an organized event, perhaps a half marathon to give a best equivalent event length as Diner en Blanc. There are plenty of threads on the forum about running a race. You could easily just run 13.1 miles in your neighborhood instead of running in the race but many choose to run in a race, similar to the informal picnic vs organized picnic argument. Yet, I don't think any appear in the Antimustachian category. In fact, I typically see them in the "throw down the gauntlet". Like Diner en Blanc, the race also has an entry fee where you can't participate without paying. Security will check that you have a bib. Course restrictions limit what you can wear. You can't be late for the start time and the event has a time limit to finish.
But here are the differences-- Races have a huge impact on others and the environment. Have you see how much trash, discarded clothing, empty cups, gel packets, energy bar wrappers, etc are left behind at the race? Cleanup takes a long time. The food and drink packaging is ONE TIME USE ONLY. Yes running clothes, and shoes are reusable but so are the white clothes as Diner en Blanc.
But run that race if it is your goal to or attend a Diner en Blanc... Afterall...
The question is never whether or not someone else's choices are inline with your priorities, but whether or not their actions are inline with their own priorities.
***. This whole argument is void if you are in deep debt. Debt removal trumps all other values/goals.