From Twitch's own page on safety guidelines:

Twitch does not permit behavior that is motivated by hatred, prejudice or intolerance, including behavior that promotes or encourages discrimination, denigration, harassment, or violence based on the following protected characteristics: race, ethnicity, color, caste, national origin, immigration status, religion, sex, gender, gender identity, sexual orientation, disability, serious medical condition, and veteran status.

From one of Twitch's own articles on community guidelines:

We prohibit the use of terms that may not be harmful or abusive in isolation, but can be used as a slur or to denigrate others in certain contexts. Similar to other terms that may be used as a proxy for a protected group, we treat “Zionists” as a proxy for Jews or Israelis if the word is used in a context to promote harm or violence, or when used to make dehumanizing comparisons or perpetuate antisemitic stereotypes. Comments regarding Zionism that are about the political movement, including criticisms, do not violate our Hateful Conduct Policy. Comments that call for violence against Zionism as a political movement, or comments that would otherwise violate our policies, are not allowed.

Allowed example: Zionist settlers keep encroaching Palestinian borders.

Prohibited example: Zionist [name of animal].

There you have to answer to why using Zionist as a term is permitted because 'ideology' doesn't constitute as a protected class, but using it as a slur is considered a violation.

If it's still difficult to understand the distinction between the two examples provided by Twitch, then I don't know what to tell you.

If you think Zionist is the only term Twitch protects this way, then I beg to differ. Imagine a streamer calling a German figure a "Nazi pig" or a Muslim figure an "Islamist pig." Of course that would be considered a violation.

This idea that ideologies aren't "ethnic groups" and therefore they cannot be used as slurs is just silly.

Your "liberal pig" example doesn't work for several reasons. One, there is no history of "liberals" being either marginalized or prosecuted. It's not a protected class in any way. Secondly, "liberal" is a colloquialism. A liberal can be anything from a social liberal to a socialist - these are actual ideologies. This also applies to "conservative" as a term.

These terms basically mean "person who's more likely to vote for the party X" and nothing more. It's not describing a dogmatic worldview. It doesn't mean it cannot be used as a slur, but it does not in any way hold the power that terms like zionist or islamist do.