I don't know about kefir but I passed loads of what you described for about five weeks before things cleared up. I did not even know I had candida until my 4th liver cleanse. I did a coffee enema after my 4th liver cleanse and the next day the white stuff started to come out. I have done a couple of parasite cleanses and Bowel Cleanses prior to that but didn't see any white stuff.
The amount of white stuff that came out scared me at first but It's been 2-3 weeks now and I feel much better even with normal diet. What has helped me the most has been improved diet, oregano oil, P&B shakes, coffee and plain water enemas. Have also been taking a product called "Symbiotics, Candida Balance" which has helped tremendously. I also took a few drops of Colloidal Silver under the tongue for 3 days in a row. Don't know whether it was the Colloidal Silver or not but on the 3rd day I got the worst stomach cramp followed by a semi painful diarrhea and passed tons of white stuff along with a lot of white powder. It has been a couple of weeks now that I have not seen any white stuff even after doing enemas and feel so much better with much more energy.