They do say science advances one funeral at a time. 
In reality, people are convinced by arguments regularly: when what is being argued for doesn’t dramatically contradict their existing beliefs and/or comes from someone they like, or a respected authority figure. Older scientists are often strongly invested in a particular theory and may never change their mind, but younger ones who don’t have entrenched beliefs are open to alternatives. I assume the same is true in other contexts - younger people, and especially children, will be more open to new beliefs.
Ideas can spread from the top down - as people are more likely to adopt beliefs held by those of high status - and person to person: hearing an idea from multiple people around you means you are more likely to accept it, regardless of anything else. I think your idea of hearing a fact incidentally, rather than in the context of a debate, fits with this process. Depending how foundational the belief is, you may see people actually change their minds, as happened with opinions on gay marriage, or it may be only younger people who grow up with the new ideas who are convinced and it changes with the generations, as AFAIK we are seeing with decline in religiosity.
But the ‘people around you’ mentioned above have to be part of your ‘in-group’, as do the experts. Neither of us would take very seriously arguments from the Ayatollah of Iran, for example. Nor are you likely to be influenced by what random Trump supporters say online. However, if you have conservative friends and neighbours, you are likely to be influenced by their views, and vice-versa, as long as you see them as part of your ‘tribe’.
A phenomenon I have witnessed repeatedly is the person who is part of some identity group - usually religious or political - who finds themselves in disagreement on an important issue. For religions, this will usually be questioning some aspect of theology. Due to the intolerant nature of such groups, the person may end up deconverting and being ostracised by their former peers, and when they do, they will often adopt diametrically opposite beliefs on a whole range of issues. I think it’s because their old ingroup and trusted authorities have been discredited in their eyes, and so they become receptive to ideas they would have rejected without seriously consideration before, as well as being surrounded by a new peer group who normalise them
Something similar may be happening with the conspiracy theorists: they come across evidence an authority figure has lied about something, or showing a generally-denied ‘fact’ that happens to be very convincing to them, and this radically changes their view of who is their ingroup and outgroup. Other conspiracy theorists become their new peers; accounts promoting conspiracies, anon or not, are respected as experts in place of the real experts from wider society. This would explain the dramatic switch from trusting the experts to rejecting everything they say.
And I think trust issues explain why a lot of conspiracies that used to be bipartisan or more common on the left, like anti-vaxxing, have now switched almost entirely to the right. Distrust in authority used to be prevalent on the far left, but as it has become clear how socially liberal and thus Democratic-supporting the majority of intellectuals and academic experts are, right-wingers are less and less likely to see them as part of their tribe and thus someone to listen to, while left-wingers have become more likely to trust them.
And at the end they will often deny they ever believed X. But yeah, if debates work, it’s usually slowly, and probably accompanied by knowing other people who believe in ‘not-X’. Honestly, I think anecdotes are probably more effective at changing minds, especially if they invoke an emotional response. Journalists always seem to try to include a few in their stories.
. But realistically, I’m going to suffer the same biases as everyone else.
