A few months ago we tried on the offchance to get a Műzekart and were politely told by the staff at Selçuk museum that only Turkish Citizens were entitled to one. More recently we heard this rule had changed and a friend of ours had managed to get one. Currently there is no indication of this rule change on the Műzekart web site which still states that applications from non-Citizens will be refused. More helpfully the website lists many of the places where a Műzekart can be used, it is not a complete list, and there are some exceptions which are clearly listed. All the exceptions are areas within sites where you have to pay extra in any case (e.g. the Harem at Topkapi and the Terraced Houses at Ephesus).
With this potential change of rules in mind we walked into the museum in Selçuk and asked, expecting to have to try to explain there is a new law which means that people with a residence permit and kimlik numbers are now entitled to one. We were pleasantly surprised, not only were the staff aware of the new rules but knew exactly what needed to be provided. We were asked for Kimlik Numbers and Residence Permits, and paid 30 lira each. No photographs were required, the photos in our Residence Permits were scanned and used for the card. There are no forms to fill out, everything instead entered onto computer. Our local mobile number was taken and it was explained we may be called for security reasons, so we guess having a local phone number may be necessary. The whole process took less than 5 minutes.
To summarise, what you need:-
Contact telephone number
The cards are valid for one year and give free entry into virtually every museum and archaeological site in Turkey under the aegis of the Ministry of Culture and Tourism. For us, this represents a significant saving. We will be making a great deal of use of these.