To begin with, I'm going to answer the question in the title. Yes, there are mere symbols. One can make up arbitrary symbols and use them to stand for trivial things. So in the grand scheme of things, there can be mere symbols.
But here's the more interesting question: When people think it is important to say, "Such-and-such is a mere symbol," are the symbols in those cases really "mere"? Herewith, a few examples.
A few weeks back, I got an e-mail from somebody about an old post I wrote at Right Reason that discussed, inter alia, cannibalism. My correspondent said that he doesn't think cannibalism is always wrong, because what we do or don't do with a person's dead body is only a symbolic matter. So, for example, cremation isn't intrinsically wrong but might be wrong if you meant to symbolize by it a disbelief in the resurrection of the dead. He gave as a further example a wedding ring. A wedding ring symbolizes your vow to your spouse, but that doesn't mean that there could never be odd or extreme circumstances in which it would be morally licit to take off your wedding ring and even to hide your marriage. That wouldn't have to mean that you didn't really love your spouse or weren't really committed to the marriage, because the ring is just a symbol.
And then there's the flag of our country. We sometimes hear, "The flag is just a symbol."
Finally, to get really controversial, there is the memorialist position on the Eucharist, according to which the bread and wine are, in the words of an Anglican author (who was denying the memorialist position) "bare symbols" of Christ's body and blood.
Now, an interesting thought has occurred to me. Suppose you believe in God. Or--to stretch the point as far as possible--suppose you don't believe in God, but you do believe that what people believe, say, or intend about matters of great importance is itself of great importance. It seems to me that a consequence of this is that in one sense there are no mere symbols for things of great importance.
What do I mean? Take the wedding ring. While I won't deny that there could be weird circumstances in which it was allowable for you to hide your marriage, under most circumstances, it isn't. And having once put on your wedding ring, it would usually be a sign that something is very wrong if you start deliberately going around without it, unless there is some physical reason why you can no longer wear it. Imagine a man who, contemplating leaving his wife, stops wearing his wedding ring and starts keeping it in a shot glass instead. Such an action would mean something. It would be a dishonoring of his wedding ring and, by extension, of his wife and his vows to her. It would be an outward and visible sign of an inward and spiritual declension. I think even a pagan could see this. Since marriage is important, what we say about marriage is important.
If you believe in God, this point becomes even more evident. Suppose you are a low Protestant and don't believe that marriage is, in the Catholic sense, a sacrament. Still, you believe that God heard your wedding vows. Those vows were saying something--making a promise. And the ring represents those vows before God. So if you act like the man in my example, what you are doing is in essence blowing a raspberry at the God who witnessed your wedding vows.
How about the way we treat dead bodies? Well, something similar applies: I happen to believe that cannibalism is always morally wrong. But I don't believe that cremation is always morally wrong. Still, I think it's to be avoided when possible. And I think that how we treat dead bodies is a very important matter. Some months back a friend visited me and told me about how she accidentally found herself and her children at an "art" exhibit of plasticized human cadavers posed in all sorts of ways--as a ballet dancer or a tennis player, etc. She was somewhat shocked, but not nearly as disturbed by the idea as I was, and I hadn't even seen it. She kept saying how interesting it all was. I said something like, "But look, you're a Christian. The burial of the dead is one of the corporal works of mercy. Dead bodies shouldn't be treated as art objects!" She hemmed and hawed a bit and told me that, after all, even most Christians don't believe in the corporal works of mercy. I'm still not sure why that was supposed to matter; perhaps it was supposed to absolve the maker of the exhibit from the charge of deliberate wrong-doing. (As if he didn't know it was "edgy" and sensational.)
The point is that saying, "How we treat a dead body is just a symbol" is actually not true and is rather dangerously untrue. Because man is made in the image of God, the way we treat a dead human body says something about something important. And what we say about things that are important is itself important. Does that statement give us rules for how we are to treat dead human bodies under all circumstances? No, it doesn't. It doesn't tell us whether dissection, vital organ donation, cannibalism, cremation, and any of a number of other actions are always wrong, sometimes wrong, or never wrong. But it does tell us that these questions are important ones, because a dead human body isn't just a bunch of atoms and how we treat it is a serious matter.
How does this point apply to the Eucharist? Well, it certainly isn't going to come even close to resolving the differences among various schools of thought--memorialism, receptionism, non-transubstantiation Real Presence, consubstantiation, transubstantiation. And I am not saying that those differences are trivial or to be brushed aside. But there is (at least to me) an interesting point to consider: The memorialist himself doesn't really believe that taking Holy Communion is a "mere symbol." He doesn't really believe that, because he thinks it's a very important thing to do. He believes (this was dinned into my head during my entire childhood) that in taking Communion he is saying and showing something--namely, the Lord's death. He also believes that he must do this in obedience to Christ's command. And what we say and do about things that are very important is itself very important. So, for example, the memorialist--at least the old-fashioned kind (maybe not the kind that meet at Kent's church)--believes that Communion should be taken reverently and with contemplation of Christ's crucifixion, that it should be done regularly, that he should confess his sins before it and thus prepare himself for it, and that he should be (in the words of the Prayer Book) "in love and charity with his neighbor." Some Baptists, if they are teetotallers, may think you can do it with Welch's grape juice, but you'd never catch them doing it with Coca-Cola. What we say about important things is important, so they are careful to say it with decorum and seriousness. Which is worth something, and which says that they are not, even by their own lights, engaging in an act that is "merely" symbolic.
Years ago I was a smart-alecky nineteen-year-old. Sitting at dinner with an elderly missionary who had been my pastor when I was six, but who had seen little of me in the interim, I listened to him talking about how when he was a pastor he would reprimand people he caught smoking on church grounds. "I would tell them, 'This is God's house, and it's not appropriate to be smoking in God's house,'" he said. I was suddenly seized with an attack of devil's-advocate-itis. After all, thought I, this man doesn't believe in Sacraments. He doesn't believe physical places can literally be holy. What business does he have making such an argument against smoking in a church? In only slightly more polite tones, I made this argument to him. I got my comeuppance in the end, though: He told the assembled company, "She just likes to argue about everything. She was always that way, even as a little girl." That was embarrassing.
And I was wrong. At least, I was wrong to give him a hard time. Whether he was guilty of any formal theological inconsistency, I'm not sure. But he was on to something about the building. Scripture--which Baptists believe in passionately--makes it clear that it is possible to dedicate places and objects to God. And then the principle kicks in: How we treat those places and objects says something about what we think of God. The Bible envisages a day when the very bells of the horses will be inscribed with the words "Holiness unto the LORD." It is clearly no accident in the Book of Daniel that the fatal hand writes "Mene, mene, tekel upharsin" over Belshazzar's reign just after he has dishonored the vessels of the Temple at a drunken feast. And Jesus drove the money-changers from the Herodian Temple, crying, "It is written, my house shall be called a house of prayer. But you have made it a den of thieves."
This argument resolves few practical difficulties. But it does mean that we should think twice, and more than twice, before we shrug and say, "But that's just a symbol."