I have had this problem off and on for this second beta round. The first one I think I encountered this once.
If I start INS from steam, I often encounter getting kicked by anticheat. This is typically resolved by going to the INS steamapps folder and starting insurgencyeac.exe manually. When I do that, I usually don't have any issues with EAC, but this is not always a fix.
Additionally, the load times that are discussed here are not the issue that I've encountered with EAC. I happen to sit next to someone with almost identical hardware, except the hard drive in one machine is a platter drive versus solid state. Each system experiences this EAC issue.
Something else experienced with getting kicked due to the false-positive is that I am only kicked once I spawn.
There are times I will join a co-op match, be able to select my gear, but have to spectate for a short time between objectives; as soon as I spawn, I will be kicked either immediately, or after a few minutes of play as described by @facknrite.
In general starting up the game requires me to either go through several crashes, or several EAC-kicks before being able to play through any matches.
Edit: Forgot to mention, the person that I sit next to transferred their installation to an SSD. This was done because loading from the platter drive was too slow, allowing someone else to take the player slot in a co-op game; Because of this, they would not be able to spawn, or even select a team. Instead the user is forced to spectate and is unable to select a team (for the given team available in co-op).
This is happening for myself and another person locally on the same LAN.