I'm under the impression that it's better to donate to the distro(s) that you like, rather than the foundation. The foundation gets all that big corporate money and a lot of the distros don't get very much.
Is this thinking flawed?
Nothing wrong with doing both. Linux wouldn't have the market penetration that it has without the work of the foundation. Keeping a massive opensource project on track is kinda like herding cats. Solid distros are important but what has made Linux an economic force is the fact that it is everywhere (android, routers, set top boxes, media players, etc).
To the OP I am already a member but if they allow paying membership dues in BTC I will renew mine in BTC.
From their website
Does the Linux Foundation store my credit card information for the annual recurring charge of the membership dues? The Linux Foundation does not store your credit card information. The Linux Foundation uses the opensource project Ubercart and Drupal to administer registrations. Ubercart uses Paypal as the payment processing gateway. When you sign up as an individual member, a recurring Paypal profile is created on Paypal's servers to administer the annual recurring charge.
One thing to find out is if there are any
ubercart integration solutions for Bitcoin. If they can drop in integration through bitpay or coinbase and be up and running quickly that may influence their decision.