I don't think that people finding things to support their own views from available 'evidence' is new phenomenon rather I'd suggest that where there tended to be an establishment view that was accepted by a majority of people on the majority of issues, the lack of trust is more widespread. That we've had PMs and cabinet ministers talking about being stymied by the establishment is indicative of this.
Added to that, the availability of information and disinformation has expanded exponentially, and while that should make us more careful about evidence, because of how we seem to work it makes us less so.
When Yeats wrote in The Second Coming:
"The best lack all conviction, while the worst
Are full of passionate intensity",
it was talking about the general phenomenon here but I think the world we live in has reduced doubt so much more because it has become what we fear most.
I am constantly aware of warnings through history about the concern of change, and novelty, and how so many times they have been not sufficiently justified but not all of thise warnings have been completely wrong, and we have changed little, if at all, while the pace of change is ever faster.
To go back to Yeats:
"And what rough beast, its hour come round at last,
Slouches towards Bethlehem to be born?"
I agree with a lot of what you say. However, being realistic I would say that diversity occurs because it is useful - some people with passionate intensity for abstract ideals are necessary to counter-balance other people with passionate intensity for an opposing view or to counter-balance people with a passionate intensity for money or power or personal-self interest or to counter-balance dispassionate ruthlessness or despotism etc
Human emotional and intellectual diversity being a product of nature / nurture means there will always be some people with passionate intensity for something that others passionately disagree with. Hence I think civilisation requires for example both religious and atheists to keep each other in check and mitigate the dangers of human tunnel vision and group think, and help the continuation of the species.
I would say widespread distrust of the establishment seems a normal by-product of periods of political and cultural change, hence the point I made about the increasing distrust of the establishment in the US during the Vietnam war. The culture in the US was changing due to the Civil Rights movements of the increasingly politicised black community, and young people were becoming less inclined to accept the establishment narrative that shipped them off to fight a conflict in Vietnam, especially where black people were disproportionately represented in the army as cannon fodder, fighting for a country where they were treated as second class citizens. The establishment attempted to fight back by labelling dissenters as Communists.
I see some similarities today in attempts to label as Hamas supporters or terrorist sympathisers those who mistrust the establishment's narrative on the Zionist-Palestine issue. Being against the Zionist position does not mean an automatic endorsement of Hamas terrorism. I may agree with some of what Hamas is saying, some of what the Zionists are saying, and also disagree with both groups on their positions on various aspects of this conflict. If the establishment narrative is that Muslims need to denounce everything that Hamas is saying, that's just not going to happen as I myself don't see any of these issues in terms of black and white or good guys vs bad guys.
I personally don't accept the establishment narrative that it is morally ok to turn a blind eye to the killing of thousands of civilians to get back about 150 hostages. I think that is a morally bankrupt position to hold. I distrust the establishment narrative and the narrative of Israel's supporters who say Hamas and not Israel are responsible for the thousands of Palestinian civilian deaths.
On a more general point, I think increasing interaction between differing cultures lead to cultural change followed by changes in leadership. Leaders will have to incorporate some of the ideas expressing distrust of the establishment in order to get sufficient political support to maintain their positions of leadership.
The Mongol Empire in the 13th and 14th centuries was one of the largest land empires in history. Initially ruled by Mongol tribes following traditional Mongolian shamanism and tribal customs under Genghis Khan, the empire eventually adopted Islam as the main state religion during the early 14th century. As more trade occurred between the Mongols, Persians and Arabs, Mongol leaders and soldiers gradually converted to Islam for practical reasons relating to commerce and alliances. Mahmud Ghazan for example, leader of the Mongol empire in the 13th century, converted to Islam after significant interaction between the Mongols and Muslims. One motive behind Mahmud Ghazan's conversion to Islam was a desire to attract the support of those Mongols who had already converted to Islam in order to overthrow a rival.