Trudeau is actually still wildly popular with the overall populace, as the reaction to his reappearance during Meech Lake and the last referendum, as well as to his death, made quite clear. He's just rather unpopular on this board for various reasons.
Without him leading the Liberal Party, it seems quite likely that Pearson's successor would lack the star quality to win a dominating majority in 68. Stanfield wasn't a great media sensation but was generally respected; a Liberal leader without the equivalent of Trudeaumania might still win, but just yet another minority government (and I'd say it's unlikely Stanfield could win a majority either), which at this point had been standard since Diefenbaker.
This might have some interesting butterflies in how government was perceived. In OTL, the Liberal party under Trudeau absolutely dominated the 70s (Clark's cup of tea nonwithstanding), the first half of the 80s, and then came back under Chretien to dominate in 1993 for another decade, and Brian Mulroney's Conservative interregnum was also two dominant majority governments. This made a lot of people only really familiar with the idea of majority governments, how they worked, and how they treated (and were treated by) the opposition. How Martin and Harper's minority governments have been treated, and what expectations people have of them, I think are greatly affected by this (most notably, the general public expectation seems to be that the government should govern like it has a majority even when it doesn't; there was little public pressure on Martin or Harper to even look like they were compromising, and they both obliged).
But if government stays in a pattern of being mostly minority governments, usually propped up by strategic NDP support, there will be a lot more expectation of compromise and retreat from ideological purity from the governing party. This might keep the PCs especially more ideologically mixed; the lack of Trudeau would also reduce (though I doubt completely remove, due to economic factors) the rise of Western (Albertan) alienation and the populist fiscal/social conservatism that made up the core of support for Reform/Canadian Alliance/current Conservative party. This could lead to a scenario where the current political scene is considerably less radicalised than it is today (though the US is likely to still end up more and more politically radicalised, which would affect Canadian politics as well). Still, any scenario which leads to Red Tories still being a viable force in the party is probably good for Canada overall.
How Quebec goes in a no-Trudeau scenario is anyone's guess; any Anglo prime minister succeeding Pearson could even very conceivably lead to a Levesque-led separation. At the very least, I expect a lot more upheaval in the province, which is saying something.
Canada almost certainly is going to be less socially liberal without Trudeau's influence on the national stage. I don't expect us to beat the US to the punch on legalising gay marriage in any non-Trudeau timeline. It'll pretty much set back socially liberal causes a few years to a decade across the board. That might have some interesting butterflies since it's one of the things people point to to show how Canada isn't like the US, but Canadians have pretty much been using the US as a bogeyman (while simultaneously trading with them and eagerly consuming their culture) for a century, so I'm sure we'll find something else to highlight our kind of insignificant differences.
Without Trudeau, the Constitution may or may not get patriated (I'd say probably yes, but maybe not until the lates 80s or early 90s - I also can't see many people other than Trudeau doing it without Quebec's signature being on it somehow, necessitating it only happening when a Liberal government is in power in the province); it will almost certainly mean Canada follows a less independent course in international politics, likely continuing just to support the UN and/or US in most issues. We'll still be generally liked, but somewhat less of a distinct entity.
So overall, I'd say the result is: less radicalised politics and a survival of the Progressive Conservatives, Canada is more invisible on the international stage, a somewhat less angry Alberta, and a more angry and quite possibly at least partially sovereign Quebec (although full separation is still pretty unlikely for a whole host of reasons). Canada is overall less socially liberal, and has something less of a "national identity".