What makes it difficullt at the moment is that most EDA packages were developed for Windows (for obvious market reasons), so there's very little for Linux in terms of commercial solutions.
Cadence is an exception, as they have long offered tools for Linux - actually some of their tools were even Linux-only (like the microeletronics design tools).
But, if the company must not be western AND have Linux-compatible software, you're asking for a needle in a haystack.
Though, I would still have a look at Zuken products - maybe they have something now that can run on Linux, who knows. Didn't check recently.
But, as a side note, "neutral" Linux doesn't mean much unfortunately. There's no such thing. Even with KiCad - sure it will usually run properly on most distributions, but the KiCad team only supports a couple of them officially and if you use any other, you're on your own - they won't help you, and you can say goodbye to their pro support if you need it.