Can Catholics who are vegans eat the Eucharist?

That depends upon how you define “meat,” and what you believe. For despite Catholic claims of taking Scripture literally as regards the Lord’s supper, and speaking of the Catholic Eucharist as being the “true Body of Christ and his true Blood,” (CCC 1376; 1381) with bread and wine having been “substantially changed into the true and proper and lifegiving flesh and blood of Jesus Christ our Lord,” being “corporeally present whole and entire in His physical ‘reality.’” (Mysterium Fidei, Encyclical of Pope Paul VI, 1965) "the very body which he gave up for us on the cross, the very blood which he "poured out for many for the forgiveness of sins,"(CCC 1365) the fact is that in Catholic Eucharistic theology “this is My body…blood” is not taken purely literally.

The presence of Christ's true body and blood in this sacrament cannot be detected by sense, nor understanding, but by faith alone..." (Summa Theologica; Summa Theologica - Christian Classics Ethereal Library)

"If you took the consecrated host to a laboratory it would be chemically shown to be bread, not human flesh.” (Dwight Longenecker, "Explaining Transubstantiation")

For “this is My body…blood” to be taken purely literally would mean that the apostles at the Lord’s supper would have indeed be consuming the same literal, manifestly incarnated body and blood of Christ that was crucified, which manifest physicality is stressed in Scripture, in opposition to a Docetist-type Christ who is materially not what He appears to be. (1 John 1:1-3)

Instead, akin to the latter Christ, if not precisely, the Christ of the Catholic Eucharist materially appears to be what He is not, that of ordinary unleavened bread and alcoholic wine. "The Most Holy Eucharist not only looks like something it isn’t (that is, bread and wine), but also tastes, smells, feels, and in all ways appears to be what it isn’t." (The Holy Eucharist BY Bernard Mulcahy, O.P., p. 22)

But which bread and wine themselves are held as no longer existing when the priest utters the word of consecration “this is My body….blood.”

"Every theological explanation which seeks some understanding of this mystery, in order to be in accord with Catholic faith, must firmly maintain that in objective reality, independently of our mind, the bread and wine have ceased to exist after the consecration, so that the adorable body and blood of the Lord Jesus from that moment on are really before us under the sacramental species of bread and wine." - Pope John Paul II, Ecclesia de Eucharistia, 2003

Meaning that the point of Catholic sacerdotal priestly consecration (which office is itself not Scriptural) it is to be believed by Catholics that "true body" of Christ is present under a "new mode of being, " that the invisible substance of the bread and wine are changed into the body and blood of Christ. That at consecration the substance of the bread and wine is changed during the Eucharistic consecration into the Body and Blood, soul and divinity of Christ under the appearance of bread and wine, while His body in its spatial existence in Heaven remains, with the "accidents" [a philosophical term referring to appearance] of the bread and wine replacing the accidents of Christ’s body: his tissues, bones, and cells. Thus "While Christ’s body is in heaven according to his natural mode of existence, it can simultaneously be present in the Eucharist according to a supernatural mode of existence." (http://www.catholicvirginian.org/archive/2013/2013vol89iss3/pages/article7.html)

Which is to be believed even though the Eucharistic species still looks, feels, behaves, and would taste and test as actual bread and wine, and thus such decays even though it is said to no longer exist.

At which point the body and blood of Christ are no longer said to be present as the Eucharist either.

(CCC 1377: "The Eucharistic presence of Christ begins at the moment of the consecration and endures as long as the Eucharistic species subsist." "...that is, until the Eucharist is digested, physically destroyed, or decays by some natural process." ibid, Mulcahy, p. 32)

A t which point it seems that neither the decaying bread or wine nor the body and blood of Christ really exist in that time and place. (Summa Theologiae, Question 77)

Therefore, according to both Eucharistic theology as well as scientific testing a vegan would not be consuming the same literal manifestly incarnated body and blood of Christ that was crucified. And also, according to the same evidence of physicality that would prove the Son of God was incarnated, then the bread and wine are just that, and actually exist after consecration, and thus both decay as well as being a problem for some persons with celiac disease, an immune reaction to eating gluten, and the Catholic church forbids gluten-free wafers (though low-gluten wafers can be allowed by the local bishop, as well as for low-alcohol wine).

However, in contrast to the Catholic metaphysical contrivance of the Lord’s supper, the Scriptural understanding of this ordinance is metaphorical, in which the members show/proclaim the Lord’s death for them until He returns by sharing food with others whom Christ purchased with His sinless shed blood. (Acts 20:28; 1 Co. 11:17–34) Thereby effectually remembering His death for them, and showing the unity with Him and each other (as being “one bread” themselves: 1 Co. 10:17).

And thus to eat independently to the neglect of others is to actually not come together to eat the Lord’s supper, and is that of not recognizing the body of Christ as being the church. As explained in 1Cor. 10,11