The way the colors landed plays out well for conservatives, who get the red pill, representing reality. I don't know if that was intended in "The Matrix." I rather doubt it. Rog Phillips wrote a science fiction story in the 1950's in which the reality-representing pill was yellow, though it was ambiguous which environment was the real one. I would protest that I don't want either pill, I want what happens without pills, but it's a literary device, and has more drama.
The men's rights movement also uses the concept in terms of red and blue pills, though I am not familiar with whether they mean that red is reality, or just "our way of looking at things." Obviously, the two will be related. I think they mean that taking the blue pill is a denial of biological reality, and imposing a created power structure by social force.
Side note: I think most people credit that men's rights advocates have some legitimate complaints, but that they include a lot of pretty disturbing people. I could say that at work without getting into any trouble. I couldn't say the same thing about women's rights advocates. There may be a punching-up, punching-down element to that. Not a fully sustainable one, given who gets to be in Congress, run for president, or be a media star, but there's enough everyday reality to keep it afloat.
Back to reality. Terrible joke, sorry. I made a FB comment a few years ago about my news feed skewing liberal, and a second-cousin replied that "reality skews liberal." I did not confront him with the later news reports that FB was indeed putting its thumb on the scale, but I did feel vindicated. Conservatives and especially libertarians feel the same way about their beliefs, that no pill is necessary. If you just take life as it is, you will gravitate to their POV. That is not only the biological reality that men's rights people assure us is more powerful than acknowledged, but the economic reality that market pressures are what naturally occurs, not an imposed system. There is an additional element of believing that human beings have long-standing ways of behaving and perceiving, whether that is inherited culture or hard-wired. Well, we all think that, of course. I think it is likely that we move in the direction of social pressure. (Though for some of us, there is a reflexive attitude against social pressure as well.) In the face of that, one would have to drift blue because of media and entertainment, unless one took precautions against it. Taking a red pill, for example.
One of my arguments against liberals is that they do have many house-of-cards beliefs, that reality can be remade or reimagined with just a little (government, expensive) effort. The replication crisis in the social sciences is not going to undermine conservative beliefs, after all. Even if undermined by enormous destruction of their evidence, few liberals will change their minds, but that's how we all are. My argument against conservatives is the mirror of that. Too many believe that there's not really any way to change things, so let's not even try. I am in agreement with them that reality is not as malleable as the educated folk seem to believe. However, we are not the same men and women as even our near ancestors. There are continuities in personality and culture, sometimes over enormous periods of time, certainly. That alone suggests they may not change much, or not reliably. Yet even I find passages from colonial diaries strange, not quite understandable.