This was an unusual paragraph in which I disagreed with every sentence. I hope you won't mind if I respond point by point.

This is why I'm generally against unpaid internships, especially those that don't seem like education is their priority.

Do you not trust the worker to determine what benefit they get from a working arrangement, and whether it is worthwhile? Isn't volunteering a laudable form of unpaid work that can provide benefits unrelated to education?

I find the situation where one has to live and work unpaid for months or even a year just to have a chance at getting gainful employment to be coercive.

The cost of rent or food might compel someone to work more or accept comparatively less advantageous working arrangements, but most people do not consider such facts of life to be coercive. Who is doing the coercing? Many people feel compelled to spend many years and a lot of money on education so they can earn a better living in the future. Are they also victims of coercion?

We all, left or right, seem to agree that coercion is wrong, but we seem to disagree as to what it consists in.

I have tried to define the word, but have not seen you do the same. In particular, I would like you to explain how someone who voluntarily accepts a working arrangement, and is free to abandon it the moment any better alternative becomes available, is a victim of coercion. Who is doing the coercing?

I would say that any market that demands unpaid labor is coercive.

The "market" does not demand anything; the market is a place where people meet to offer and make exchanges. "Demand" in an economic sense is nothing more than being able to say what you are willing to exchange for something. Starbucks demands $2.40 in exchange for 16 ounces of coffee. Some people demand 16 ounces of coffee in exchange for $2.40, and a deal is made. Some people don't want coffee that much, or already have plenty of cheap coffee or tea, so they "demand" a price of zero. Nobody is under any obligation to give them free coffee.

One can say that there are other industries that don't demand such situations, but then the free marketer is going against his own assumption that a laborer will find the thing that (s)he is good at and fill that niche.

No one tells the journalism major to pass on the internship at Condé Nast and work as an astrophysicist instead, since it pays better. The assumption is that the laborer will try to find best opportunity available, given their skill set and other realities.

It appears to me to be an undue barrier to entry that automatically excludes less well off workers.

Your position suggests that we prohibit people from considering one possible means for gaining work experience, without considering whether they have a better alternative. The worker can already choose to decline an internship if they have a better option. If they choose to accept it, and you step and prevent the arrangement, your behavior is clearly coercive and, in my view, a barrier to entry that particularly applies to the less well off who have fewer alternatives.