Is it illegal for uninvited recyclers to come on private property to go through refuse bins in CA?

It's trespassing, but the police are not likely to get involved unless there are substantial incursions onto your property, entering gates, etc. At least that is my experience in the Bay Area. When you put the cans out on the curb, two things immediately happen: 1) all of the CRV materials are removed from your blue bin; 2) the family of 12 next door crams the black bin with trash that they couldn't fit into their own bin.

Well they sit in the driveway(the bins) of this small 4 apartment complex. (I leave my recycling in the gated portion as I do the work to take care of it and take the bin to the recyclers once a month) Also I am not even sure that one of the neighbors has NOT given them permission to collect what they want. They do not leave a mess. I am just concerned because I let my dog out in the back yard from time to time and sometimes the gate is left open by other tenants.

I think, it is legal to go through people's trash, when the bins are on the street/edge of property, because there is the expectation that they have relinquished ownership. You don't say what kind of "private" property. A store or apartment complex may be privately owned, but open to the public. A single residence is less open to the publich, i.e. may be limited to a walkway leading to an entrance.

It is illegal. A) they are entering onto your property and B) once anything is placed in the bin it belongs to the state. The state cares a great deal about recyclables, they make money off it.

It's illegal anywhere- it's trespassing, causing a public nuisance, and disturbing the peace.