I think people mostly mean "i disagree with it politically" when they say something is "political" though. If they disagree with it politically, then it's "political".
By using those two websites, you can easily find the definition of a writing system, which is "[...] a method of visually representing verbal communication" and reflect on the fact that since emoji aren't used to encode an oral message, they don't form a writing system.
Emoji certainly classify as related to a "linguistic system" even if you don't think they have a direct verbal counterpart. Non-verbal languages certainly exist and many of them have forms of writing systems and some of those are encoded in Unicode, too. Emoji isn't the only "writing system for a non-verbal language system" encoded in Unicode.
The codepoints obviously still need to be kept distinct if they are to inter-operate.
Emoji's are already segregated in their own codepoint ranges. If emojis are what you are annoyed by?
You're just suggesting that, like, entirely different personnel be involved (they may already be), or we give a different name to the emojis, just to, like, register your political displeasure with them?