Try to see the positive aspect: at least these people have a vague idea that Iranians/Persians might NOT be speaking Arabic, even though the script looks the same to them (and me).

They are doing a lot better than the woman who asked a Polish friend of mine about all those Polar bears that she was sure Poland was overrun with. Or those who think that everybody rides around on camels in Iran. ;)

I think this is a real problem here in the United States.
Because of the conflicts our two governments have most people here in the US look at Iran superficially, and lump them together with the Arabs because of the location and common religion.  Most Americans have never heard the word 'Farsi', and certainly have never been taught the rich and proud heritage of Persia, its culture, literature and art.  
I am convinced the only way to have peace in the world is to keep talking, keep learning about each other, keep seeing that at the heart we are all the same.

Try not to be too hard on my (sometimes) ignorant countrymen.  Most of them mean well :-)

Who is 'they?'

You should remember that the middle east is a very complicated region of the world. Most people don't make a study of that part of the world. A few specialists at universities and governments and think tanks study this area of the world. Normal, everyday people don't. They have no reason to.

No one can know everything about every country in the world.

 I am always a little surprised that educated foreigners don't know that the US started out as English colonies. But again, it's a huge, complicated world. Just because something is important to me doesn't mean that it has any meaning to anyone else.

You might be interested to know that there are many Americans who believe that the US state of New Mexico is part of Mexico!

So I don't think there's any reason for you to be miffed at those who don't know that Persian is the language of Iran.