Resident Oriental Orthodox ("Non-Chalcedonian", if you must) checking in, as I see the Eastern Orthodox have already been (I wasn't sure if non-Catholic/non-Protestant views were welcome until I saw that, since this is "Denomination Specific Theology").
We also teach that we are the one true Church, but in the sense of having kept the Orthodox faith (read: it's not like our Lord Jesus Christ established the Coptic Orthodox Church
in particular, as He did not preach in Egypt that we know of, but this
is that Church in Egypt, Libya, etc.). I wouldn't necessarily echo all what our EO friend has said, but there is a sense in which we agree with and can say that we know where the Holy Spirit is, but not where He is not. It is more common at least in the modern day to say that the Chalcedonians are fellow Christians, just not with us because of doctrinal disagreement that we have by and large worked out
theologically (via the OO-EO dialogues), but have stalled in working out
practically.
And Catholics and Protestants are largely considered similarly (i.e., same as any other Chalcedonians, since that's what Protestants are, having inherited that from their mother Rome), albeit more 'modern' and hence with more differences. We actually once had a entire Lutheran family visit us at my parish in Albuquerque, NM, and I don't think I ever had a more awkward Agpeya meal after the liturgy than that one. The vast difference in
theology and accompanying mindset was really hard to miss, to the point where even one of my friends (an Egyptian) said to me afterwards "Who talks like that? Those were some weird people." It isn't really attributable to culture, as I was certainly more culturally akin to the our Lutheran visitors (I'm not Scandinavian or whatever, but I mean that in the sense of being non-Egyptian, 'White' Americans), but I was still just as mystified as anyone else as the wife of the family keep babbling on about her experiences with stigmata (unknown in Orthodoxy), visitations by angels, etc. I remembered from my own time in Catholicism before discovering Orthodoxy that some Catholics -- 'Charismatic Catholics', I take it -- that some Catholics talked like this, but I always thought
those people were weird, too. Many strains of Western Christianity, broadly speaking, tend to encourage these kinds of ecstasies, whereas in Orthodoxy (and in the Coptic tradition more specifically, being so heavily rooted in monasticism) they are cause for concern about demonic influence/attack if they are indulged. (This is probably why things like stigmata never manifested among the Desert Fathers or others.)
Roman Catholics and Protestants definitely need to sort out historical and doctrinal grievances among each other, for their own sakes, but approaching Orthodoxy would be something different. We're not the one true Church
because you aren't, but because the faith has been preserved among our fathers and handed down to us to this day with great sobriety, clarity, mystery, stamina, and the instruction and protection of the Holy Spirit, Who is God.
From the Agpeya (Coptic Horologion/book of daily prayer), Prime hour:
THE FAITH OF THE CHURCH
One is God the Father of everyone.
One is His Son, Jesus Christ the Word, Who took flesh and died; and rose from the dead on the third day, and raised us with Him.
One is the Holy Spirit, the Comforter, one in His Hypostasis, proceeding from the Father, purifying the whole creation, and teaching us to worship the Holy Trinity, one in divinity and one in essence. We praise Him and bless Him forever. Amen.