I solved this problem in a tricky way. And in a tricky way I've got it, I gues.
I took my old master branch I worked on some time ago and now decided to carry it commit-by-commit in to my new project. And it seems that back in days I messed around with my file modes between one commit and another.
So after consistently creating theese commit files for move-over by hitting gitk
s "Write commit to file" I've started to "git apply" commit- files one by one while editing some of them in notepad.
Here is a sample of fix that worked for me.
I tweaked such parts
index 30d5c59..63e26fb 100755
to make them look like this
old mode 100644
new mode 100755
index 30d5c59..63e26fb
Hope this would help someone else.