With the preface that I'm not an Andalusia specialist, but rather have looked far more at Egypt, the Levant and Persia, the answer is that it really depends.

The first thing to point out is that the Sharia as it exists today is a very poor indicator of historical activity. Islamic law for Sunni Muslims has a number of sources: the Quran itself, emulation of the prophet Muhammad, collective consensus (often reflecting traditionally accepted practices), and analogical reasoning.

Emulation of the prophet is based on the recollections and collected sayings of the prophet covering virtually every aspect of his life and assembled into collections of hadith.

The problem is that these collections (let alone the legal norms and jurisprudence associated with them that we can actually identify as Sunni Islam) don't emerge until hundreds of years after Islam is first revealed in the 6/7th century.

From the perspective of Sharia this sometimes makes Islam look "better" from a contemporary Western perspective than it would have been in practice in and sometimes worse.

On the "worse" scale: the Sharia basically says that non-Muslims must either pay the Jizya, convert, or die. Despite the confidence of the jurisprudence on this matter, it didn't happen. This was just not how the Arab conquests worked and we have quite a lot of evidence that conquered peoples were presented with all kinds of different terms and accommodations to Arab rule.

On the "better" scale: the above being said, it's easy to exaggerate the merciful benevolence of the conquerors presented by some of the religious sources (or in contemporary Islamic apologia, which is a separate matter altogether.) It was once in vogue among historians to suggest that heterodox Christian groups (e.g. the Copts in Egypt, or Nestorian Christians) would have welcomed the Arab conquerors on the basis of their religious toleration. There is precisely zero contemporary evidence to suggest this was the case while there are accounts that describe the Arab armies as hostile invaders.

With that sort of preface out of the way, what would these relations have actually looked like? As I said, it really depended. In the very early conquests there are theories that the Arab conquerors may have tried to present themselves as being part of the same community of believers as their new Christian subjects. Regardless of whether you buy into this idea, the reign of Abd al-Malik marks a departure as state construction of religious buildings, most notably the Dome of the Rock, are accompanied with religious propaganda messages that present on contrast or appeal to Christians rather than a unified community.

The administrative relationship changed over time in other ways as well. Initially the Arab conquerors simply co-opted local Christian administration. Again by the reign of Abd al-Malik (although earlier as well) administrative reforms meant that the bureaucracy more exclusively conducted its business in Arabic. This was accompanied by an Arabization and Islamization of the elite positions of the state.

From the perspective of inter-faith harmony then, it really depends on what standard you are applying. The Medieval Islamic world would not be a politically acceptable state for most modern Westerners. That being said, in comparison with other political systems at the time, the medieval Islamic world was usually quite a bit better on issues of religious and minority rights than medieval Christendom was. This was both a reflection of the positive rights afforded by Islam to religious minorities as well as the fact that heterodox versions of Christianity simply did not threaten the state in the way that they did in Christendom. This was reserved for Islam's own religious heresies and heterodoxies (including Shiism, though by no means intend this to be a disparaging description) which of course resulted in turmoil and various forms of persecution.

In terms of harmony of the faiths, pogroms and massacres did occur in medieval Islamdom, but were not the norm. Pressure to convert, however, was quite real so while you could maintain your faith and still be a powerful prosperous individual, over time voluntary conversion to the ruling religion becomes the norm in part because of the social/political/economic structures in place that eventually encouraged conversion.

I hope that goes some of the way to answering your question, in terms of sources In God's Path by Robert Hoyland is excellent on the conquests, while The Venture of Islam by Marshall Hodgson is a massive history of Islamdom complete with quite a lot of social history.

Apologies again that this is more general than Andalusia focused.

Edit: the above also leaves out mention of Jews, for whom the position would have been more stark. While an orthodox Christian would have had fewer rights (also, the language of "rights" in this context is incredibly anachronistic but that would require another divergence) under Islamdom than in orthodox Christendom, Jewish life, especially in Spain, prospered as the community had equal status with other religious minorities rather than their almost uniquely persecuted, regimented or restricted position in Christendom, although I'm sure a European medievalist would be more familiar with the status of Jews under Christian rule than I am.

edit 2: some typos