Did some Christian sects ever hold the opinion that ritual slaughter was obligatory, before the 10th century?

Many of the Christians in the areas and times mentioned were likely previously Jewish or Islamic or would have been familiar with some other form of ritual sacrifice by records if not by direct application. Such exceptions seem to be made whenever convenience dictated it.

While related to the Samaritans at the time of Christ, It is quite possible similar rules were put in place by the Islamic world in relation to Christians who could at least be taught the "right way" to do things.

A Samaritan egg, as the hen laid it, could not be unclean, but what of a boiled egg? Yet interest and convenience strove, by subtle casuistry, to invent excuses for what intercourse was unavoidable. The country of the Cuthites was clean, so that a Jew might, without scruple, gather and eat its produce. The waters of Samaria were clean, so that a Jew might drink them or wash in them. Their dwellings were clean, so that he might enter them, and eat or lodge in them. Their roads were clean, so that the dust of them did not defile a Jew’s feet. The Rabbis even went so far in their contradictory utterances, as to say that the victuals of the Cuthites were allowed, if none of their wine or vinegar were mixed with them, and even their unleavened bread was to be reckoned fit for use at the Passover. Opinions thus wavered, but, as a rule, harsher feeling prevailed.

Geikie (Life and Words of Christ, vol. 1, pp. 495–6), omitting his citation of authorities.

Also:

To the orthodox Jew of the time a Samaritan was more unclean than a Gentile of any other nationality. It is interesting to note the extreme and even absurd restrictions then in force in the matter of regulating unavoidable relations between the two peoples. The testimony of a Samaritan could not be heard before a Jewish tribunal. For a Jew to eat food prepared by a Samaritan was at one time regarded by rabbinical authority as an offense as great as that of eating the flesh of swine. While it was admitted that produce from a field in Samaria was not unclean, inasmuch as it sprang directly from the soil, such produce became unclean if subjected to any treatment at Samaritan hands. Thus, grapes and grain might be purchased from Samaritans, but neither wine nor flour manufactured therefrom by Samaritan labor.

Talmage (Jesus the Christ, (2006), pp. 172–3).

Curiously, in parts of the Holy land, this practice is maintained to this day. See: "There is no role for animal sacrifice in Christianity," by Jill Hamilton. Apparently, there is a custom in the Palestinian village of Taybeh, some 30 km north of Jerusalem, of Christians offering sacrificed lambs in the ruined Byzantine church of St. George:

"Around 70 to 80 lambs are sacrificed here each year," said the Roman Catholic priest, Father Raed. Similar sacrifices are also made in the towns of Lodd, Jaffa, al-Khadar and elsewhere in the Holy Land.

(...)

The Catholic priest in Taybeh assured me that he himself did not take part in the sacrificial rituals, but neither did he condemn them. "The meat is distributed to the poor and to our old people's home. It is a tradition," he added.

The author goes on to climb in a soap box to denounce the practice, although she does not explore how, if at all, the sacrifice practice differs from the profane butchering of animals for food. She mentions that the sacrifice is done "as in Halal butchery", and quotes the mayor of the town saying that "sometimes sacrifices are offered as gratitude for the birth of a healthy child, help with a relation surviving a deadly illness or a major operation, or thanks for survival from a car accident."

Regarding the validity of the practice, she quotes the expert opinion of a Palestinian archaeologist, Dr. Ali Qleibo:

Qleibo, although a Muslim himself, insists that Christian blood-sacrifice cannot be explained away as a Muslim influence: "Blood sacrifice was an important part of the ancient Canaanite religion and numerous pagan cults. Semitic blood sacrifices have persisted."

It is possible that some of the early Muslims might have made contact with some of these para-Christian practices, although I would not be so quick to dismiss Muslim influence — even assuming that the practice predate Muslim domination, it is frankly highly unlikely that it would be by chance performed the same way that Halal rituals demand.

I do not know if this response will actually answer your question, but I will give it a possible conclusion to it.

In a sense animal sacrifice and ritual slaughter are not always clearly seen or defined, yet it would seem inappropriate to have a animal sacrifice without a set ritual for slaughtering such animals.

Rituals of animal sacrifice have been far more common in Christianity than is generally recognized. When missionaries arrived in Britain around the year 600, sacrifice was so deeply engrained in culture that the Pope allowed it to continue provided that the animals were offered to the Christian God and no other. In more recent centuries, these rituals have been mainly confined to Eastern Orthodox Churches. An ancient sacrificial liturgy known as the matal, meaning ‘something tender’, has persisted In the Armenian Church to the present day.

A key requirement of animals offered for sacrifice is that they must be unblemished, ensuring that they have been well-fed, comfortably accommodated and free from disease. In the Armenian matal, at least three factors minimize the suffering caused to the animal during slaughter: rules must be observed, attentiveness shown by the slaughterer, and reverence displayed at all times. In some accounts of sacrifice, the animal is presented as so contented that it co-operates in its own sacrifice. Paulinus (354-431) describes such an instance at the shrine of Felix of Nola in southern Italy, in which a heifer designated for sacrifice guided her owners to the shrine to present herself with them. - Christian Attitudes to Animals

There is the Armenian Matagh tradition that persists to this day. It should be noted that according to tradition, Armenia became a Christian nation in the Year of Our Lord 301.

In Armenian Christian tradition, matagh (Armenian: մատաղ mataġ) is a lamb or a rooster slated for sacrifice to God, a ritual which has continued from the pagan past. In many regions of Armenia today, this pagan-Christian synthesis is very much alive in the regular slaughter of chosen animals in front of churches. Matagh is done often to ask God for either forgiveness, health, or to give them something in return. People generally gather at the house where the Matagh was done, where they pray and eat the meat. Tradition holds that the meat must be eaten before sundown.

It is not impossible that the Ethiopian tradition of slaughtering animals while saying the trinitarian formula predates the 10th century.

In the 7th century the conquests of the Muslim Arabs cut off the Ethiopian church from contact with most of its Christian neighbours. The church absorbed various syncretic beliefs in the following centuries, but contact with the outside Christian world was maintained through the Ethiopian monastery in Jerusalem. - Ethiopian Orthodox Tewahedo Church

Wikipedia has this to say about Christian dietary laws:

Slaughtering animals for food is often done with the trinitarian formula. Although the Armenian Apostolic Church, among other Orthodox Christians, have rituals that "display obvious links with shechitah, Jewish kosher slaughter." In addition, meat consumed by Christians should not retain any blood, a practice that both Jewish and Islamic methods of slaughter also prescribe, and one that is done by most slaughterhouses throughout Christendom. - Christian dietary laws

Today this tradition can still be seen in Ethiopia, the only question is as to when this tradition was first implicated.

In Addis Ababa, there is one Christian slaughterhouse and one Muslim one, each of which supplies all respective butchers and restaurants. At the Christian slaughterhouse, an Orthodox priest will bless all the animals with a Trinitarian blessing, a pattern that is repeated in other large towns and cities. In the countryside, this may be left to the senior male householders who pray a Trinitarian blessing over the bull, goat, lamb or chicken before its throat is cut. - Food & Fasting