No they don't?

https://www.gov.uk/foreign-travel-advice/iran

There is a british embassy in Iran. https://www.gov.uk/world/organisations/uk-for-iranians In fact the foreign office advises against all but non-essental travel for British-Iran dual nationals. For british citizens there is only a recommendation against travel to certain parts. For many other citizens it's, arguably, even safer.

It's particularly challenging for people Iran might deem to have Iranian nationality (dual nationals obviously, but also people who were formerly or are eligible for Iranian citizenship but don't currently claim it), but otherwise a lot of the restrictions are more "our government doesn't like their government and wants to reduce trade", not actual safety risk to individuals. Unlike NK, Iran has generally not detained purely US persons who were on group tours. If there were some flare-up in tensions, sure, you could become a diplomatic problem, but otherwise it's probably safer than many other countries as a visitor.

As a tourist from the Netherlands I've been to Iran in 2015, and have not had any unpleasant encounters, other than a taxi driver really wanting my business. He was brushed off by other taxi drivers.

Even the more religious individuals I've encountered, were always very open and pleasant to converse with. My opinion was that there is a big divide between the Iranian I've encountered on my tour, and the position of the Iranian government.

Actually, I've found the people much more pleasant than in any other country I've been a tourist in Which includes the UK and the US.

If you're from the US or the UK I believe you're going to have some trouble getting in, and diplomatic assistance will not be done by your own embassy, but by a friendly one. Once you're in, you shouldn't have to worry about anything other than enjoying the beautiful country.

All this is except the obligatory headscarf situation. Which is really bad. If you can personally get over that, it's a great place to visit.

The level of threat is less than visiting in Egypt or some other common western tourist destination.