While Interest Groups were are certainly a way to back some political idea, or another, there is also strength amongst the Pops, as well. There is a reason the French Revolution happened, after all.
The way Political Movements, that is changing any aspect of a country's political scene, works, is that Interest Groups will provide Support for the Movement based on their Clout, while Pops provide Support based on raw numbers, compared to the population as a whole, meaning that a single discriminated Laborer backing a Movement provides just as much Support as a fully enfranchised Aristocrat when taking action outside their Interest Group, as they are then just another Pop.
In other words, while Political Strength still plays an important role in Political Movements, in the form of Interest Groups throwing their Clout behind movements championing laws they like, it is entirely possible for a Political Movement to form with no Interest Group backing at all - even if nobody is willing to champion workers’ rights in the halls of power, enough angry workers in the streets may just be enough to affect change anyway.
Which Interest Groups will or will not back a Political Movement depends on whether they would approve of a change to the new law, in case of Enact/Restore Movements, or disapprove of the current change in progress, in case of the Preserve Movement. Interest Groups that have high approval or which are part of the Government will not support Political Movements, though Government IGs may put pressure on you in other ways if they’re not pleased with your actions.
Pops are more complex, as they can back a Political Movement either because it aligns with their political movement, that is their preferred Interest Group is in favor of the movement, or because they have something to gain directly from it, for example, a discriminated Pop backing a movement that would give them more rights.