It does not matter if the Statue reminds us about freedom, or France, or poverty, or Trump's immigration policy, or copper and atoms - all of these are just thoughts and interpretations.
What matters is, are these thoughts harmonious ("conducive to peace" in Buddhist lingo) or do they have an element of dis-harmony in them, a seed of conflict or clash ("conducive to suffering"). Any time there is clash, there is suffering (assuming we take it seriously). This includes situations like e.g. the ethical or philosophical conflict between the Statue's Poem's message and the current immigration policy. This clash is a conflict of ideas in your mind and is a type of suffering. This also includes situation when two people with two conflicting sets of ideas look at the Statue and attempt to discuss what they see/think. If they are serious about taking their sides, the clash between their interpretations becomes suffering for both.
The point is, reification of our interpretation as reality is what actualizes the clash and makes it into suffering. Being acutely aware of the basic mechanism behind perceptional and interpretative conflicts leads to a more philosophical stance which does not create the basis for conflict and suffering.
Hence "the map is not territory" - because when we remember that map is mere map, we don't fight over whose map is reality (conflict=>suffering!), and we don't get frustrated when the landscape in front of our eyes mismatches our map-driven expectations (conflict=>suffering!).
So it's not about so-called "objective" (scientific) observation vs. symbolic meaning. It's about the relative nature of any and all observation, and not getting caught up in it as a way to peace.
The next question to ask is how does the Buddha see the Statue of Liberty and how should we see it if we want to be like the Buddha. At the first approximation, the right way to see the statue is from phenomenological perspective, as a stimulus for the process of interpretation. Thus the phenomenological perspective is the Buddhist equivalent of your seeing in terms of atoms - what scientific materialists would call the most objective mode of perception. Retaining mindfulness of the perceptual mechanisms at all times is an important stepping stone in the Buddhist practice.
The real perspective of Buddha is far more radical than seeing things in terms of their phenomenology. To explain this point, let me draw a parallel between our perspectives and the planetary model of atoms. If we compare any single interpretation to a specific location of the electron, then the Buddha's perspective is like seeing the entire electron cloud as its orbital function. Buddha integrates all known factors of interpretation without collapsing them into one simplified position.
This is why Buddha's perspective is not "conducive to suffering" and is as "conducive to peace" as possible - because the orbital function is never in conflict with any single position of the electron. Meaning, Buddha's perspective is never in conflict with any single human perspective, it is a superset of whatever is actually valid in each of them.
As my root guru once said,
Buddha is like a lawyer - sees situations from all sides at once.
Now, since you tagged your question with Four Noble Truths, let me map this back to them. Suffering is that experience when something is perceived as irreparably "wrong". The nature of suffering is conflict between "wrong" and "right" (or actual and expected, which is same thing). Origin of suffering is attachment to one of the sides and declaring it "right", "the way things are supposed to be". Cessation of suffering is peace that comes from not creating the conflict, through not attaching to a side, through transcending the limits of simplified positions. Path leading to cessation of suffering is methodical application of the principle of not creating conflict and the causes of conflict, hence not creating suffering and the causes of suffering - from coarse, to intermediate, to subtle.
Not creating long term causes of conflict is tricky. It's definitely NOT being a pushover always accepting other opinions. As said, it requires being above one-sided opinions, and in touch with reality behind all perspectives; being able to translate between different views. Above all, it requires being consistent at NOT letting confused one-sided agendas drive one's behavior.