I was born in Iran in 1970. Will I be allowed to visit USA now? Have visited before with work, as cabin crew, but have not attempted entry as a visitor. I am hoping to go soon. I have a British and Swedish passport. They both show my place of birth. I do not want to go there with any risk of not being able to go beyond passport control. Can you please give me some guidance? I am still cabin crew but only domestic and Europe destinations now. Not sure how things are now since Trump. Look forward to hearing from you. Many thanks in advance.
Since you are not a national of Iran and have not been in the country since before 2011 (or, indeed, before the 1979 revolution that soured Iran-USA relations), there should be no effect on your ability to visit the USA.
You can apply for an ESTA like every other Swede or Brit.
The good news is that you can almost certainly visit the US, however it is very possible that you may require a visa to do so.
The first thing you will need to confirm is whether or not you are an Iranian citizen. You almost certainly believe you are not, but at least officially it's possible that you are based on the fact you were born there. Wikipedia has a page that describes the basics of whether you are likely to be an Iranian citizen. Based on the basic details in your question I suspect you are not a citizen, but you'll need to confirm that.
If you ARE an Iranian citizen, then you are not eligible to use the Visa Waiver Program, and you will need to apply for a US Visa, although (again, based on the basic details in your question) this will likely be approved.
If you are NOT an Iranian citizen, then you should apply for an ESTA. As a part of this process you will need to state your place of birth (Iran) and your citizenship (NOT Iran!). It is likely that your ESTA will be approved, but also very possible that it will not be - in which case you will need to apply for a visa. For this reason I would suggest applying for the ESTA well before you plan to travel in order to give time to apply for a visa if required. (ESTA lasts for 2 years).
When entering the US you may face additional scrutiny due to your place of birth, but presuming you've been truthful on the ESTA application then you should be admitted to the US.