Parubiy hadn't been a member of Svoboda for over a decade. Even more importantly, he resigned a couple of weeks ago, so he's not currently even in any position of power.
Yarosh had never been the second in command in the National Defense and Security Council.
Serhiy Kvit is not a member of Svoboda or Right Sector. Neither are Tetyana Chernovol or Dmytro Bulatov.
Oleg Makhnitsky and Ihor Tenyukh have long since resigned their positions.
The only individuals affiliated with Svoboda who are currently in charge of a cabinet ministry or position are Oleksandr Sych, Andriy Makhnyk, and Ihor Shvaiko. Right Sector has no members in the cabinet, nor any elected members of parliament.
So that's a grand total of three Svoboda in the 20 person cabinet. You don't have to be an expert in math to know that's well short of the "nearly a quarter" claim in your Foreign Policy piece you cited.
And yes, the Azov Battallion does seem like a disturbing group. However, they're not government sanctioned--they're neither Army nor National Guard. They're a private militia, so it's rather disingenuous to claim that they are the neo-Nazi face of the Ukrainian government. They're also rather small--estimated to be only about 300-600.
Yes, unfortunately there are some actual neo-Nazis living in Ukraine. The fact of the matter is that there are neo-Nazis living just about everywhere. Including--as we all know--our own country.
But if you do want to talk about neo-Nazis in a position of high power in Ukraine, we're more than welcome to talk about Pavel Gubarev, who was a prominent member of Russian National Unity (identified as being a neo-Nazi organization) and who has looked back with great fondness and without any regret with his affiliation with that group. The problem is, he's not fighting for the Ukrainian government--he's fighting against it. In fact, he's the self-proclaimed "People's Governor of Donetsk", a position he gained not through any sort of elections, but instead by brute force.
Now, think about it: If the pro-Russian separatists claim all they are doing is fighting "fascists" in the Ukrainian government who they claim gained power "illegitimately", and yet one of their most prominent members is an actual fascist who gained his power illegitimately, do you honestly think that's the real reason they are fighting?