Generally abysmal, with a small period of relative peace.

The two main theaters of muslim-christians relations were the Spanish in the west and the Romans in the east. I can't say much about the spanish front, except that the Christians and muslims in spain generally hated each other's guts, at least on a state level. My main interest is in Eastern Roman history though, so that's where I'll focus. Keep in mind that pre-crusade muslim history is almost 500 years long so this might be a little bit of a long read.

To start, 90% of the former christian lands that ended up in the caliphate were taken from the Romans. The original arab invasions happened right after the last great Romano-Persian war, where both sides were absolutely exhausted from their 30 year death struggle. The Romans put up an initial fight with what little they had left, but after that failed they were forced to hole up in Anatolia while The levant, egypt, armenia, north Africa, and what little was left of roman spain were taken. Eventually the arabs attempted a serious siege of Constantinople in an attempt to get rid of the romans for good, but that failed miserably so the arabs gave up on trying to take territory and decided to continuously raid Anatolia instead. They also occasionally supported rebel emperors who would be more favorable to them, though this rarely worked.

After a few hundred years of raiding the caliphate started collapsing and the romans started regaining their strength. It was only after this point that hostility between romans and arabs started to simmer down. During the macedonian period (850~ to 1025) there were multiple technological exchanges between the Romans and Muslims, especially the moors in Spain, there was even a mosque built in Constantinople to accommodate Islamic officials. Trade between romans and arabs also increased drastically, leading to increased cultural tolerance. All in all this period was pretty good for muslim-christian relations in the east, though there was still hostility, especially at an individual level.

These relations started to break down after Basil II, the last macedonian emperor, died with only his incompetent aged brother, Constantine VIII, as his heir. After the death of constantine there was a period of crisis (5 emperors and 2 empresses in 60 years) where the economy of the roman empire took a nosedive, and with it went the army. It was during the height of this crisis, in 1071, that the roman empire was invaded by the seljuk turks, who also happened to be invading pretty much everyone else at the time. The turks were much less tolerant of christians than arabs were, and they ended up taking the levant and almost all of roman Anatolia. They were oppressive to native christians and refused christian pilgrims access to the holy lands, which further increased roman resentment of them.

It was under these conditions that the first crusade was called (it wasn't really supposed to be a crusade, the roman emperor just requested some extra soldiers but the pope went a bit crazy for legitimacy's sake) with the nominal purpose of reclaiming Anatolia for the Romans and the holy land for Christianity. As opposed to a response to islamic aggression, the first crusade was more of a response to Seljuk aggression and intolerance.

Well that's a brief history of islamic-roman relations.

TLDR: hated each other for a while, then didn't, then started hating each other again.