Recently I have been writing a question at https://christianity.stackexchange.com. I have noticed that browser underlines word “eucharistic”.
As I am neither English nor catholic, I do not know any rule for capitalisation of the word.
Is there some rule for that or is it just a catholic custom to appreciate the idea behind the word?
There is no hard rule. Adhere to the discipline of your editor, publication, or organization, or in the absence of a house style, adopt a style manual appropriate to your audience and tastes and be consistent in its application. In other words, there is no single standard. For what it’s worth, the Religion Stylebook published by the Religion Newswriters Association (RNA) capitalizes Eucharist but is silent on adjectival uses:
Eucharist A term commonly used by Roman Catholics and Eastern Orthodox Christians and High-Church Anglicans for Communion, but some Protestants use it as well. In the Holy Eucharist, the Lord Christ is contained, offered, and received in the form or presentation of bread and wine. See Communion.
The word Eucharist may encompass many different concepts: the sacrament and its related doctrines, a type of worship celebration (also known as the Mass, Holy Communion, the Divine Liturgy, the Lord’s Supper, and so on), a specific part of of that worship service (the Liturgy of the Eucharist, but also to the distribution of Holy Communion), or to the sacramental food and drink distributed at that service (held in Catholic, Orthodox, and High Church traditions as the Body and Blood of Christ).
Because in Catholic belief, the Eucharist (as sacramental food) is synonymous with the Body and Blood of Christ, reference to it is consistently capitalized. The style guide for the Archdiocese of Milwaukee is typical:
sacraments Catholics and Orthodox recognize seven sacraments. The word sacrament is lowercase. Capitalize only Eucharist, lowercase all other sacraments: baptism, confirmation, penance (or reconciliation), matrimony, holy orders, the sacrament of anointing of the sick (formerly extreme unction).
Adjectival uses, however, are lowercased, e.g.
eucharistic adoration Always lowercase the term eucharistic adoration.
The Episcopal Church style guidelines are very similar:
sacraments Capitalize the proper names used for a sacramental rite that commemorates the life of Jesus Christ or signifies a belief in his presence: the Lord’s Supper, Holy Communion, Holy Eucharist. Use lowercase for the names of other sacraments: baptism, confirmation, penance (sacrament of reconciliation), matrimony, holy orders, and the sacrament of anointing the sick (formerly extreme unction).
In practice, things are a real jumble, even in official documents specifically on the topic referring unambiguously to the consecrated host (yet another term), e.g. USCCB
[J]ust as natural food gives nourishment to the body, so the eucharistic food gives spiritual nourishment.