According to http://www.pbs.org/funding, tax dollars pay for about 15% of the budget across all PBS stations. And a large part of that money goes to ensuring that local stations can exist in places that they otherwise couldn't. While tax dollars are helpful, in no way are they paying for that content in the same way that the BBC is funded by people in England.
In any case the reason for that geographical restriction is that PBS makes money from selling access to popular shows like Sesame Street worldwide. They could not make that money if organizations in that area had no incentive to pay for it.
...it's more like I'm paying for something but getting nothing.
My taxes help to pay for the system of embassies and consulates that provide a support network for people like you. Since I live in the USA and have no plans to travel, I'm getting nothing from that tax money.
Welcome to a fundamental fact of taxation, most of what our taxes pay for does not directly benefit us. Nor do we individually have any say about how that is spent. Once it has been taken by the government it is in no real sense "ours". Get over it.
That makes sense for things that are targeted at a particular audience, geography, etc. But television? They had to spend money to implement the blocking feature, and seemingly for no additional money they could let people in Europe watch. I'm not asking for special treatment. And I'm not interested in watching Sesame Street, but rather programs which are not offered for sale (I'd even pay $0.99 per episode, if I could).
As a side note, if you want services from a US embassy, you often have to join a days-long waiting list, and then pay rather high rates for the services. Contrary to popular belief, it's not a place you just walk into because you're a citizen and they do things for you. It's more like a state-owned Kinko's plus law office in a prison-like setting. I appreciate your point about your taxes paying for them, but you should know they aren't giving me anything for free in there.
PBS is not a government organization. It is a private non-profit organization that is free to do what it wants. In this case you have a classical problem. Developing quality programming has a fairly high fixed cost and low marginal costs. Yes, they could cheaply give it to you, but if they did then they would lower the incentive for non-US organizations to absorb some of the fixed costs.
The fact that they do not sell it to individuals who want it is a sign that they are missing a great business opportunity. It is stupid. But again it is not government stupidity. (And for the cost of an EC2 instance to use as a proxy, you can get around the geographic restriction.)
And what about the tax money? Tax money that goes to PBS stations largely goes to the geographical problem of supporting local PBS stations in locations that do not have a sufficient donation base to pay for it themselves.