I decided to post this topic, because it was very hard to found in the web, but the solution is pretty easy.
1) Install proper ethernet kext's, be sure that they are working properly.
2) Be sure that EthernetBuiltIn chameleon option is DISABLED
3) Download EFIStudio 1.1
4) Click on "Select device", select "Ethernet"
5) Click on "Add device"
6) Hex number will be shown in the window. For example, it looks like:
7) Edit your org.chameleon.Boot.plist. Add:
<key>device-properties</key> <string>MY HEX</string>
Where MY HEX is hex number you just obtained from EFIStudio.
8) Reboot, and enjoy your first App Store login
Maybe it's architecture-independent, but I got this problem on AMD hackintosh, so I publish it here.