I don't think that's true. If you simply removed the de facto state endorsement of parties - if you only listed candidates by name on the ballot and moved to a California type open primary instead of having partisan primaries - you probably wouldn't end up with two parties like we see today.

Party primaries are a good example of this. They're also FPTP, but that hasn't lead to the emergence of two subfactions because such a thing is hard when it's not entrenched in the ballot. Instead primaries have much more loose coalitions of groups and endorsements that shift around in every election. Even in a particular election there are often more than two.