Yes, keep questioning what you see in the world around you. Life unquestioned is life lived in a religious state. A belief may blind you to different points of view, so its up to you to broaden your knowledge.
It's incredibly comforting to have safe beliefs to rely on, so much so that it can be taken advantage of. Instead of resting on them, it's better to move away from that comfort zone and taking the risk of discovering you may have been wrong about it, and learn something new from it.
It's ok to challenge what you see, and having doubts can help you grow alongside other people while discussing with them, rather than having firm convictions leading you in a narrow stagnating nowhere.
Questioning is one thing, knowing how to get the right answers is another. And so is believing that something extremely familiar and widely believed/present even needs questioning.
Humans have limits. And what we can do in our environment has limits, even now. It is good to encourage not becoming complacent and dependent. But no one wants to always, 24/7, every single minute of their lives, having to be paranoid, skeptical, accomplishing everything all by themselves. That is called surviving, not living. We survive because we HAVE to, not just because we WANT to as if it is a hobby.
You want to live life to enjoy it and relax at least sometime not to always work and worry just because. Because that is comfortable and makes life worth living. Not just because we are lazy, but we are biologically and psychologically wired to crave comfort.
It is not only not feasible for us to always question everything like robots, but it should not have to be mandatory. We encourage independence and because it is pragmatic, not desirable in and of itself. And in this day and age, we have the networking capable of creating change that can make the world more comfortable to live in without constantly having to watch our backs.
We should take advantage of that and realize what is obstructing us from that by not only making ourselves responsible, but the sources of our problems responsible too. Or else we allow ignorance to fester. Maybe not in ourselves, but to everyone else who is not already as wise, capable, or fortunate as you are.
And this does not have to be a black-and-white issue. We should not have to pick between being skeptical and being reliant. We can use BOTH by creating the ideal resources and situation for that. There is not even a point to this debate because I mainly agree with you, but that does not mean our priorities can't work in tandem.
It makes sense to tell people that when someone or something pushes you down, you should learn how to get back up. But if we want to work together, care about each other, stay informed, and communicate, we should also learn how to push back against that threat, that bully, that predator, that incorrect source so they can stop inconveniencing people. You can run to other safe spots and reliable options, but that only gets you so far. And even having those options in the first place relies a lot more on luck and privilege that a lot of people care to admit.
Responsibility goes both ways. Towards yourself and the world around you.