In the majority Greek text of the Gospel of Luke, 23:32, the critical text reads:
'ηγοντο δε και ετεροι κακουργοι δυο συν αυτω αναιρεθηναι'
whereas the majority text reads
'ηγοντο δε και ετεροι δυο κακουργοι συν αυτω αναιρεθηναι'

I am not at all an expert, or even marginally competent, at translating Greek. However, it seems to me that these two sentences have basically the same meaning. On the other hand I have heard some say that the critical version should be translated '... two other evildoers,' whereas the majority text should be translated 'two others, evildoers.' I don't think that the word order matters here, and it seems like both can be translated as 'two others, evildoers,' even though the majority text is maybe a little clearer. Can anyone comment on the translation of these variants?

Thanks for asking this question. Both versions can be read in two different ways, as meaning "two other, malefactors," or "two more malefactors" (without commas) as if Jesus was a third malefactor. The Byzantine version (ετεροι δυο κακουργοι) favors the first reading, because it gives closely to the "other" a noun (two persons / ετεροι δυο) before the word "malefactors", which then can be read as an adjective, referring only to these two persons and not to Jesus. The King James version thus translates "And there were also two other, malefactors, led with him to be put to death."

Of course the Byzantine version can also be read as meaning "two more malefactors, besides Jesus", but this reading if favored more by the critical version. In any case, interpretation is the key factor, and interpretation here is easy. Since the Gospel is written by a faithful person, it can not mean "two more malefactors", but only "two other people, who were malefactors", which is the reading favored also by the Byzantine version.

Cf. www.ellopos.net/elpenor/greek-texts/new-testament/luke/23.asp" target="_blank">https://www.ellopos.net/elpenor/greek-texts/new-testament/luke/23.asp

Thanks - this was essentially what I suspected as well (that both could be interpreted either way, but the Byzantine is clearer).
The question arose in terms of which was closer to the original - I had heard an argument that the critical could not be faithful to the original on the grounds that it insinuated Christ to be an evildoer. But it appears to me more (or at least equally) likely that the critical is like the original and that a redactor changed the word order to clarify.

Your guess is logical. However, as you perhaps know, the question of what text is closer to the original, is far from closed. There is not even such a thing as just one critical edition. Even the majority or Byzantine text shows some variations here and there, no matter how trivial they are.

Since the New Testament is not just a text of some authors, but a text of the community of the faithful, that is of the Church, I prefer to ignore textual criticism, not because it is itself very uncertain, but because the Church by definition has more authority to recognize what is genuine and what is not in the text. After all, the Church decided even what books belong to the Canon, and the Church suggested that these books are written by these authors and not others. If I start to question the text by means of textual criticism, why should I stop there and not go on denying that the Gospel of John is written by John, etc.? Without the Church, there is no text at all.

Considered as a pure philological problem, the problem of the New Testament text is of no interest to me. Think of a person that has no interest in swimming, yet he is in search of the perfect way to swim! It is absurd. If I'm not interested in faith, what is the meaning of exploring the textual problems of the New Testament - but, if I am indeed interested in faith and I believe in Christ and the Trinity, then my problem is how to live the faith of the Church and not the faith of a text.

Oh yes, I agree - and even if we had the original text in its exact form that is all meaningless without interpretation, which must be guided by God and the Church and faith. I think it was St. Chrysostom who said something to the effect that it is best to learn from God directly, and second best to learn through the Scriptures. In any case because of issues of interpretation quibbles about exact phrasings are usually rather moot, and a far more important question is to find the meaning that is there.
Nonetheless I think that textual criticism can be of some value, not because it would never teach us anything doctrinal per se, but because an understanding of the originals is of value when studying theology; even St. Augustine (whom I must confess that I have some apprehension citing him as an authority on this matter) applied some principles of textual criticism. Also because as I recall even the Church Fathers sometimes quote certain passages with some differences. Although the letters of Paul show that this doesn't really matter, after all he often quotes the Old Testament without exactly quoting the Septuagint or having an exact translation of the Hebrew (at least from what I can tell, and from what others have told me). It is in the end just the meaning.
What you say about the canon is also interesting because I have heard some people here who want to maintain the doctrine of sola scriptura, who also want to deny any authority to the Church that defined the canon of scripture! By which I mean even the early church (since the canon was certainly pretty well settled by the time of St. Irenaeus, and I would consider it definitively settled by 367 AD or so when St. Athanasius gave his list): some people will take this canon as authoritative but refuse any authority to the opinions of these Church Fathers on interpreting it.

But, this all gets far away from the grammatical question, which was really what I was interested in, because I maintained that both readings were possible for either rendering and someone else said no...

If you are interested in the grammatical questions of the Holy Scripture, you may have a look at the EPIMERISMI IN PSALMOS by Georgius Choeroboscus. Note that Georgius Choeroboscus was an ecumenical didaskalos (teacher) of the Byzantine Church, he was called this way because he started by taking pigs to pasture (Choiros - Vosko). Since he was a man of the Church and an official didaskalos it is a pity that his work receives so little attention in modern times.

The work is freely available here; it is on the web since the copyright is long expired. Unfortunately there is only the ancient Greek text, no translation.