How different were the peoples of northern Spain culturally, linguistically etc from people in southern Spain during the rule of the Umayyads?

So what you're talking about here is a really long period. I happen to have a decent source that discusses this topic at length in some parts, but I might wander a bit here and there.

So to the beginning. If we look at the early days of conquests in the 8th century, even then the actual conquering force of al-Andalus wasn't uniform ethnically at all. When they crossed the straits of Gibraltar in 711 the troops were mainly composed of Arabs and Berbers, being ruled from Damascus by the (Umayyad) Caliph. They were very much a Berber-dominated force, and Maribel Fierro (p8) reports that the number of actual Arabs among them was pretty small, and they had a fairly privileged status being Arabs. At that time there was a fairly strong link between being Muslim and being Arab which was broken down over the years, but in those days it was still quite strong. This meant that people who weren't arabs adopted the status of clients (mawali) of an Arab tribesman or of another convert who already had a patron. Freed slaves were clients as well. So in these days islamicization went hand in hand with arabicization but there were still distinct Berber and Arab cultures.

In 739 there was a pretty big Berber rebellion in northern Africa and the Caliph sent some troops to put an end to it. Without getting too much into detail about this - it led to a big influx of Arabs around Ceuta as a Syrian commander named Balj ibn Bishr al-Qushayri, initially refused passage, managed to negotiate with an Andalusi military governor who was attempting to deal with his own Berber rebellions. I could go on and on about the political consequences of al-Qushayri arriving in al-Andalus for an entire post , but suffice to say they brought their division of Qays and Yemen (northern and southern) arabs with them, although the precise meaning of this conflict in the islamic world back then is still debated. Again, without going into too much detail they were settled (with a lot of argument and dispute) in Granada (Elvira), Seville & Niebla, Malaga, Jaen, Algeciras, Sidonia, Beja and Tudmir.

So the Berbers also had their own culture and existence and how arabicised & islamicised they were depended on whether they were urban or not. So the real cultural divide at that point wasn't necessarily just northern/southern, but also urban/rural. The Berbers did however mostly settle in tribal groups in rural areas along the frontier. Please remember that when I say "frontier" here it's in the context of the early 8th century, where the frontier was in what we would consider to be fairly southern in modern Iberia. From what we understand they were mostly autonomous although it's difficult to pull the details out of obscurity with limited archaeological work. But for example, Fierro points out that some patterns of irrigation we find can potentially be linked to Berber tribal organisation, and the existence of these tribal, autonomous Berbers in the northern rural regions is highlited whenever they rebelled against the Cordoban ruler or representatives below him.

Some of these tribal berbers in al-Andalus actually continued their existence well into the Umayyad era of al-Andalus and actually outlived it - some of the taifas after the fitna of al-andalus (the huge civil war that caused the Cordoba Caliphate to collapse from around 1009-1031) were ruled by those who gained power because of Berber tribal military resources & organisation - i.e. the Zirid taifa formed by Zawi bin Ziri. From what I understand, most of these guys survived even the reconquista and the inquisition and although they eventually lost their unique cultural identities, their descendants still live in Spain & Portugal today. But, if you were an urban Berber, you were much more likely to have been a state administrator or a scholar and thus very arabicised and islamicised.

Now, if we look briefly at the christians - sometimes you see them called in secondary sources as "mozarabs" (as arabicised christians) but really I don't like this term, especially because they certainly didn't identify as this and afaik none of the actual Andalusi literature ever uses that term. This term appears in the very late Christian sources as a term they used for Christians who emigrated to the north of Iberia but who spoke Arabic and culturally resembled Arabs rather than those with Visigoth ancestry. But it's not an accurate label as it lumps them all together culturally and linguistically, when in reality a lot of them didn't really share those histories or backgrounds.

Anyway, the vast majority of the Andalusi Christians, like the Berbers, lived in rural areas with fairly limited contact with the Arab settlers & conquerors. Ibn Hawqal in the 10th century, translated by Fierro, wrote an interesting section about these relatively autonomous Christian Andalusis:

In al-Andalus there is more than one agricultural property on which dwell thousands of people who know nothing of urban life and who are Hispano-Romans professing the Christian religion. There are periods in which they rebel and some of them take refuge in fortresses. They put up a stiff fight, for they are fierce and stubborn. When they cast off the yoke of obedience, it is hard to make them return to it, unless they are exterminated and that is a difficult, prolonged process.

Something I'd like to point out about the "extermination" here that needs to be understood with context is that the history of al-Andalus is also the history of a series of governments dealing with a long series of rebellions. These included arab muslim rebellions, tribal berber rebellions, and many others - so they weren't trying to 'exterminate' Christians per se, Ibn Hawqal is more referring to rebels that can't be negotiated with and so must be defeated by conquest.

Now, Ibn Hawqal doesn't speak about what language the rural Christian spoke but it was likely a Romance language descended from Latin since the local Andalusis weren't monolingual until the mid-to-late 11th century, and even then it wasn't truly monolingual demographically until the 12th century. So yes, between urban and rural areas, and the south to the frontier, there were certainly linguistic divides - with Romance/Arabic bilingualism being common for Christians. Indigenous Christian converts were often called muwalladun - in the way it was used then it referred mainly to people who weren't Arabs ethnically, but were born into Arabic culture and were raised as Arabs. That could be anybody, without a specific indication of religion. Jews in al-Andalus were also very arabicised and in their case, it enabled them to flourish and also paradoxically to preserve their language and ethnic identity.

Despite the rural/urban divides in culture and language throughout the early centuries of al-Andalus, by the time of the establishment of the Caliphate of Cordoba under the reign of Abdul Rahman III, an era that was one of stabilising and unifying the region, a common Andalusi identity finally emerged through the work of scholars but also through the fierce advocacy of the muslim traditions of egalitarianism which Abdul Rahman III was a particularly big supporter of. In those days there was a concerted attempt to eradicate the idea of Arab supremacy (particularly in politics), although it was an uphill battle and never quite manifested in the way that was hoped and muwallads hardly ever managed to maintain the power or positions that they were given by Abdul Rahman III in place of ethnic Arabs.

This is already a pretty damn long post, so I'm going to cut it off here. I would close by saying that yes, the frontier - that changed over time - certainly did see an impact culturally but I would argue that just as big was the divide was between rural and urban areas.