I have heard that Turks can become members of their equivalent of The National Trust, whereby they can pay an annual subscription of apprx 30TL, giving them admission to all NT sites. Is there anything like this available to non-residents.

If anyone has any info, I would be grateful.

I think you are talking about "e-devlet uygulamaları" (e-state applications). I became member to there. To become member to there you will need citizen number, if you dont have, you cant be. Non-residents have no citizen numbers, thats why i think, they cant join to there either. Its my opinion.

Thank you for the information

To my best knowledge we don´t have an equivalent of NT in Turkey.. 

but wait for those with more knowledge..

 You are referring to a MüzeKart. This is not like the National Trust (which is a non-governmental body in the UK) but a governmental museum scheme. With it you can enter museums such as the Aya Sofya, Istanbul Archeological Museum, Ephesus etc. Private museums such as Sabancı Müzesi, Pera Müzesi etc are not part of the scheme.

It is supposed to be only for Turks. Tourists definitely cannot apply. But the treatment of foreigners resident in Turkey (with tax number, foreigners ID number, and ikametgah) changes depending on the site. Some of my friends have got a card, some have been refused. At the big Istanbul sites they tend not to issue cards to foreigners. But smaller places sometimes do.