You actually can leave it out as the original comment has. But it sounds rather poetic and I think it's simpler to just leave all the elements in this case.
"They are against us and we against them" should be accepted. In English, you don't always have to repeat the verb if it's the same form of "to be." It's more poetic that way but still totally correct. Report it!
Is this in the literal sense like to be up against something, or is it to not like something and to be against it
Originally it means "facing (something, somone or the other side)". But in modern Hebrew מול is used for this meaning, physically; in some contexts both מול and נגד are used, e.g. in sport matches (English "versus"). נגד suggests a more sharp conflict; we would use only נגד and not מול for opposing sides in wars, even though it's conceptually pretty much like a sport match - only more grave.
How would you say, "I am against ..."? This section seems to all be about against a person or group of people. Can the word "נגד" be used to say against something? For example does "נגדי פיל ורוד" mean 'I am against pink elephants' ?
From en.wiktionary.com about the word נגד :
Verb: נָגַד (nagád) (dated) to oppose
Noun: נַגָּד (nagád) warrant officer, resistor (electronic device)
Preposition: נֶגֶד (néged) against, opposite
I am against = אני נגד (אֲנִי נֶגֶד - ani neged) or אני מתנגד/ת (אֲנִי מִתְנַגֶּדֶת - ani mitenagedett)