Theoretically, they could influence politics greatly by deciding what and how to translate.
I've written a bit in the past about translators and interpreters involved in European relations with the Mongols:
Was there much contact between the Crusader states and the Mongol empire?
(and I should tag u/Total_Markage here as well)
Basically in the Near East and Central Asia, there was already thousands of years of tradition of interpreters working in a highly multilingual environment. When Europeans arrived they either used this pre-existing network of interpreters, or they started learning languages themselves.
Did the interpreters have a vast amount of power? Theoretically it's possible, but it wouldn't have been in anyone's best interest to leave things out or add things to their translation. I wish I could tell you stories about interpreters falsely interpreting things, then being found out and being hauled away and executed...but did that really ever happen?
Certainly some interpreters were better than others. In one of the previous answers I linked to, William of Rubruck was sent to preach to the Mongols, and he eventually noticed that his interpreter wasn't paying much attention to him and just said whatever he felt like saying.
But normally it seems that translators and interpreters were professionals who were good at their jobs. They were powerful, but not because they could pull the strings behind the scenes and influence politics; they were important because everyone wanted to make sure that both sides understood each other properly.
Let's go with a sequel to my post yesterday on 13th century woman mystic Mechthild of Magdeburg and her book, The Flowing Light of the Godhead.
I mentioned that my username comes from her book, and gave the 14th century German along with the modern English:
Du luhtest in die sele min
Als die sune gegen dem golde
You shine into my soul
Like the sun against gold
Now, did you catch that above? Mechthild was a 13th century author, and this is the 14th century text.
FLG was originally written in Middle Low German. It was translated twice in the Middle Ages: into Middle High German, which this is, and into Latin. We don't actually have the original, but we have two different translations where we have a rough idea of the translator and a very good idea of the audience. So it makes a great case--if only one example--to witness the decisions made in a translation and the effect it can have.
As mentioned in the other thread, FLG is one hell of a text. (It includes a really spectacular vision of hell). Quite fitting with some strands of medieval mysticism, it's kind of an anthology book which contains some daringly erotic divine-love poetry among theology passages and more standard poems/prayers. For example:
[God and the Soul speak]
Stay, Lady Soul.
What do you bid me, Lord?
Take off your clothes.
Lord, what will happen to me then?
Lady Soul, you are so utterly formed to my nature that not the slightest thing can be between you and me. Never was an angel so glorious that to him was granted for one hour what is given to you for eternity.
Lord, now I am a naked soul
...Then a blessed stillness that both desire comes over them. He surrenders himslf to her, and she surrenders herself to him. What happens to her then--she knows--and that is all right with me.
(trans. Tobin, p. 62)
As above, this translation is based on the High German version of FLG. There are differences between the FLG and the Lux divinitatis ("Light of the Divinity"...which might give you an idea of where this is going). The FLG's first six books are longer than the LD; contains a book 7 that the LD lacks; some of the passages are in a different order.
What the lD skips:
The most sexual-seeming love poems between the Soul and God
Book 7's theological spectulation on self-annihilation in God, which deeply worried Church officials who feared it would lead to people believing they could flout the devotions and rules of the Church
(Scholars posit that the LD was translated before Mechthild wrote Book 7, but the text could have been added later.)
So already, you see the difference between the resulting FLG and LD. One of them goes a LOT farther than the other, and in what the Church deemed were dangerous directions.
Now here's the cool part.
We know the FLG was translated for an audience of women. The DL was translated for an audience of men. Specifically, priests.
This is probably the opposite of what you'd expect. Men fearing women's power and disobedience, right?
Well, sort of. The LD might have actually been a protective measure for Mechthild, who mentions in the FLG that she was attacked and threatened for writing her book. (She wrote it over the course of her life, so would be able to comment thus).
Latin was the official language, and it mattered. For example, when people wanted someone to become a saint, the hagiography (saint's biography with miracles) was required to be in Latin. That very much narrowed down the ranks of people who could write it to Church officials.
On the other hand, the FLG was translated into High German by a priest named Heinrich von Nördlingen and a circle of his friends. And it was translated for a nun named Margaretha Ebner, and the sisters at her convent of Maria Medigen and the neighboring house at Engelthal.
We know from Heinrich's accompanying letter that he wanted the sisters to use the FLG as a text to meditate over, basically praying and sinking themselves into the text until they reached their own type of wordless contemplation/unity with God. In addition to a view that it wasn't dangerous to have the cloistered nuns read what we generally assume was close to the original, he believed that including the erotic poems would help them accomplish this goal.
And indeed, from nuns' original writing that comes out of Maria Medingen and Engelthal, we see a decent amount of their use of divine-love poetry and experiences to frame the holiness of their convents and residents. This actually linked up nicely with how male writers were framing the women they wanted to be saints (while always placing themselves in roles of power over the holy women).
Thus, use of the full FLG became a way for the sisters to encounter God alone. It was also a way for them to assert their status as a truly religious community in their own eyes--and to the outside world.
During Napoleon's expedition to Egypt in 1798, he took along translators, most of which were secondary Arabic speakers he had captured from Malta. His MO for the expedition was to capture the hearts and minds of the Egyptian people, hoping to favorably compare himself and his respect for Islam and local culture to the un-pious and un-scrupulous Mamluk rulers. He wrote grand speeches, invoking his knowledge of the Quran to win favor especially with the imams and scholars of Al-Azhar University. Unfortunately, his translators were either secondary Arabic speakers, or of limited literacy, so his typically flowery prose was chopped into relative inanity and ugliness. This likely played a small part in his failure to win over the residents and imams of Alexandria, which would later be vastly compounded by his regional administration's taxes and violent repression of dissent.
To your point - it is clear that these translators lacked power. They were a last-minute addition to the expedition, captured under duress, and as such were of middling usefulness. Perhaps this can provide a counter-point to more "powerful" translators, who were more effective, being a part of an institution itself, instead of being basically plucked off the street without regard for competence.
Sources: Napoleon's first declaration to the people of Alexandria (in French) - this was his written speech, we do not know the exact words that were actually spoken aloud, but suffice to say it was largely botched by poor translation.
Cole, Juan Ricardo. "Napoleon's Egypt: Invading the Middle East." St. Martin's Publishing Group. 2007.