So most answers about Christian food prohibitions are going to focus on the monastic orders, meat during Lent and Fridays, and perhaps going on to talk about the weird relationship with food that many Saints, and especially holy women, had. Indeed the answer that I've been working on looked a lot like that, but then I couldn't find a book I wanted to use, and so I decided to instead focus on one particular situation in which I do not need this book for. Christian conversion movements in the early medieval periods among Germanic tribes/societies to be specific.

Among these societies horse consumption was an important aspect of pagan religious life. I won't touch on WHY that's the case as I think it is a little beyond the scope of your question. Let us just work from that premise. Now this is obviously a problem for Christian missionaries, sacrificing a few horses to Odin/Woden/Wotan and eating them doesn't really leave a lot of room for Christ/God who does not require animal sacrifices. Christianity is generally pretty hostile to animal sacrifices in general as the greatest sacrifice has already been performed. However horse consumption was called out rather specifically during the process of conversion and was strenuously suppressed in places like England, Scandinavia, Iceland, and Germany.

No less a figure than the Pope himself in a letter to St. Boniface, who was missionizing in Germany, condemned the practice as un-Christian and holding no place in Christian society. Consequently, in many of these places bans on horse meat consumption follow very shortly after conversion to Christianity. Iceland for example allowed the practice to continue for a few years after conversion, in the secrecy of one's own home, and beyond the gaze of any Christians, but it too was shortly totally prohibited in the following years. Other figures also prohibited the practice in other places. Robin Fleming in Britain after Rome says that the bans on horse consumption more or less covered Anglo-Saxon England which was not a united polity until the 10th century, well after Christianity first appeared there.

Kristopher Poole's research shows the decline in horse consumption as a result of this process in England. Before the conversion horse consumption is rare but present in sites across England, and across political boundaries, but during and after the conversion time frame it becomes significantly rarer, though never dying out completely, finally there is a slight uptick later on but it never achieved the same prominence in the archeological record that it once had. Even today on England horse consumption is extremely rare and indeed grounds for scandal if it winds up in generic meat products.

Christian anxieties about horse meat consumption are also born out in other literary sources as well beyond just papal correspondence. The sagas of Iceland, suspect as they are, capture this quite well in the Saga of Hakon the Good of Norway whose refusal to eat horse meat among his people due to his Christian upbringing sets him at odds with the people he is to rule, eventually he is forced to renounce his Christian faith, after an attempt to eat the horsemeat without eating it fails to please anyone.

So this is a relatively small and obscurer part of "Christian food prohibitions" but I hope it demonstrates to you that bans on food could take the form of something beyond no meat on Friday or monks not being allowed to eat red meat because it is "unclean".