However, I've realized they have subtly different (and mostly unrespected) meanings:
platform-independent - an adjective - "This question is platform-independent"
This describes the question as being generic, and not pertaining to a particular platform, in the same way as language-agnostic describes a question as not pertaining to a particular programming language.
This tag feels redundant - while you'd expect every programming question to be tagged with a language, and should make it clear when you don't care about the language (language-agnostic), there's no need to specify a platform, and specifying that you don't care about the platform is implicit.
platform-independence - a noun - "This question is about platform-independence".
The question is asking about how to write code in a way that works on multiple platforms
This ultimately comes down to the conclusion I've made before that adjectival tags are meta-tags, and in the vast majority shouldn't exist.
My proposal is: