1. People engage in discourse to further their own agenda
This is true, but only of public discourse, where convincing others is the primary objective. In private conversations, I believe people are much more willing to compromise.
2. Mexican’s Voting
I think that @Bones is missing a major aspect of this by ignoring the difference between illegal and legal immigrants. Conservatives support legal immigration because there is a test which virtually guarantees immigrants support the constitution, while illegal immigrants tend to be less integrated into US culture and lean much further to the right.
Both parties will always keep their current stances because no matter what, having a higher ration of legal immigration to illegal immigration will be good for republicans, and vice versa.
I believe Republicans will probably continue to support lower immigration levels to further their own interests as well. Even if they are becoming more Conservative overtime, over 50% are still voting democrat. I think there is a natural alignment between conservative values and low immigration. Immigrants will naturally change the culture which conservatives try to conserve at high levels.
3. Vaccine
Generally I agree, however I do not believe that there is a world where the vaccine would be embraced quickly by the right. Republicans have a fear of big government, and anything that sounds like it could implement a totalitarian regime. Trump created the vaccine, and he continued to push it even after leaving office. I doubt the response would have been much different even if he had been in office from the Republican side.
@Reece101 brings up a good point that the left trusts health professionals, however Fauci would have been FIRED if Trump stayed in office much longer, and the messaging may have been different. Still provaccine, but probably less vocal. I bet many of those who gave into the social pressure would have held off for longer. Remember, this is the bunch that is terrified of eating non-organic food and GMOs despite what the scientists say.
4. Commonalities
This is very true, even with very far out there things that everyone should be able to agree on. For example, take the two issues of pedophiles and women. Republicans have now accuse the left of being pro-pedophile, and have cited the fact some of them have adopted the term MAP (minor attracted person) to refer to pedophiles, and have made the assertion that this is the direction that the mainstream left is heading; drag babies to drag shows, indoctrinate their children into trans-gender ideology, and read their toddlers sex education books with graphic depictions of sex. Meanwhile, Leftists believe that Republican’s are trying to carry out an all out assault on women’s rights, and truly believe that within a couple of years the US could be indistinguishable from the handmaids tale... a book that Conservatives also claim is left-wing satanic propaganda. In fact, abortion advocates on the left say we already live in this world because women no longer have a constitutional right to an abortion, so they are cursed by pregnancy, and the patriarchy forces them out of the workforce and society as a whole .
5.
All this, when we can probably all agree that pedophiles are bad and women deserve rights. Unfortunately, it has created a bit of a reverse self-fulfilling prophecy. Parents on the far left read their children wildly inappropriate books, and take them to drag shows. The only reason this happens is because parents feel politically motivated to go against bigotry and create what they see as an open-minded child, and this would not occur in the first place if we did not make unfounded accusations which would later come to pass. Let’s just hope that the same thing does not happen with women’s rights.