So, I managed to think of some things that Equestrians back in the olden days (whatever's the equivalent to the Middle Ages back then) where a lot of their beliefs would be considered extremely controversial nowadays from our modern-era human perspective. Since then of course, Celestia's harmony overcame those barriers those beliefs might have created and Equestria continued to thrive. Keep in mind that Celestia probably looked down on these beliefs herself but was unable to do much because this was the common mindset that ponies had. Also keep in mind that this is pure speculation. Here we are:
1) Only ponies of the same species may marry and mate: A pretty common way to kick this kind of thread off. This brought forth a rather large social barrier as ponies could not understand true harmony if this were the case. A pegasi only being limited to marry another pegasi and not the one they love (i.e, a unicorn) would bring forth a shitstorm in modern-day Equestria. Especially considering the friction that might have been present between the two species still, even after the showing of Hearth's Warming Eve, the two species couldn't have just looked at each other and accepted/liked the other's habits, right?
2) The wealthy shall only marry the wealthy or common class and never the lower: This grinds my gears... or would, rather. Self-explanatory considering how haughty the Canterlot folk are, even to this day. A noble would be limited to marrying a mare with high class or otherwise suffer a rather large bashing from the others if he were to marry a... servant pony.
Funny how this is considered "classy" when it's the exact opposite. ClassLESS.
3) Unicorns rule, pegasi droll, Earth ponies just suck: I'm aware that the three species can work together and actually like each other, but the case of unicorns being the top dogs might still hold strong here. They have magic, the one thing Equestria really thrives on and is run through; although pegasi probably have their own magic, nowhere near is it as elegant and/or natural as unicorn magic, but they can at least fly. Earth ponies being the ones doing all the "dirty work" would give their species a sad name, in all honesty - nothing more than just slaves, in a way.
Can you tell that these beliefs could spawn something more than just a problem? Say... a chaotic problem? These may have held some ground to it even after the founding of Equestria which marked the appearance of Discord, directly thriving off the social barriers and some hatred/friction between everything, since everything was a head-scratcher... to the point where you would be infuriated when these barriers are put up. Eventually, over time, Equestrians learned that these didn't pan out and didn't make anypony happy and only made them as a race regress.
Feel free to add more to the list.