"both sides of the story" is already a hole. Why are there just two? Are they equally credible and valid on every issue? Do we want "both sides of the story" when it comes to the Holocaust or slavery, as we see playing out in Texas today? Do we want only two sides of the story when talking about complex policy measures or historical events?
As other commenters have pointed out, you will be in a filter bubble no matter what, because you cannot speak to every person, read every paper, or understand every point of view. Bias cannot be eliminated, only understood and corrected for.
As a militant antifascist, i still find it interesting to have some reactionary perspectives to balance the dominant narrative. Some historical examples:
- abolition of slavery in the USA was not perceived by many (former-)slaves as social progress, but rather as legitimization of a new form of "wage slavery" where your master doesn't own you, but you owe them for food and housing... moreover, prison slavery is still a thing in most countries which do not recognize workers rights for incarcerated people (France, USA, etc)
- Hitler apologists point out that US army atrocities (during and after WWII) have been mostly erased from history books; on the other hand, Hitler's atrocities have been reduced to the eradication of Jews, whereas queers, handicapped folks and tsigans (among others who have also been eradicated) are barely mentioned if at all. Hitler is also "caricatured" as a genocidal freak, failing to represent his earlier figure which is a lot closer to many of our "presidents" across the globe than is comfortable to admit. After all, Hitler was presented by the media and industry (his biggest supports) as the candidate of reason and property against unions and marxists/anarchists and their rule of the mob
- Daech and other reactionary muslim militant groups insist on the atrocities of Western "democracies" to justify their own; these imperialist atrocities are never acknowledged by eg. France/USA who pretend they're on armed humanitarian missions against barbarism and patriarchy (an argument for colonization which dates back over a century!). This invisible spot in western worldview ("let's fix human rights with more bombs") leaves plenty of room for Daech to recruit young disillusioned folks who know their government is lying and killing innocent civilians abroad
Overall, i think any propaganda slips through your brain and leaves traces, just like any form of advertisement. So i can recommend as a general rule of thumb to never read neo-nazi/patriarchal/capitalist propaganda. However, when you're studying a precise topic, i believe getting points from all sides (not just two, as you pointed out) is an important practice that can help you develop a better understanding of the issue to overcome your own conditioning.
Especially in Global North republics who pretend to be democracies (but don't have any democratic features [0]), it can be hard and painful to acknowledge that our governments don't recognize or respect any of the fundamental rights they so eagerly accuse other nations of infringing on, that all political parties and corporations running the show are delusional maniacs, and that no "human rights" NGO will save us. Sure we all have human rights in theory, but practicing them would be considerably better!
[0] No, electing overlords every few years is not a democracy. Those electoral systems were precisely (historically) designed to prevent democracy which was seen as a danger to the 18th century elites.
As other commenters have pointed out, you will be in a filter bubble no matter what, because you cannot speak to every person, read every paper, or understand every point of view. Bias cannot be eliminated, only understood and corrected for.