I just flew to california two weekends ago and this was my experience....
In order to limit the time spent waiting in lines I printed out my bording pass online. When I arrived at the airport I checked in my luggage at the curb. So, all I had left was the stroller, my baby sling, a diaper bag ( consisting of diapers, wipes, some factory sealed snacks, and a bottle of milk), along with my purse. My baby was sucking on her bottle during the security line and when it was my turn to go through it, I was asked to dump out my baby's milk!!!!! I was shocked because my daughter was drinking it. It was heartbreaking to have to take it away from her. Immediatly after I dumped it another security employee told me that Milk was okay and the two security employees started arguing over it. Meanwhile my daughter is still out of milk :(. Once I got through the security checkpoint I was able to purchase some more milk at McDonalds. I was then able to keep my baby in her stroller until it was time to board. Just before boarding I put the baby in a sling and checked in the stroller. I actually kept the baby in the sling the entire flight. On the return flight I was told that slings or baby carriers were not allowed.
Good luck!