People who say "two state solution" can be broken down into three camps:

The ignorant. Been told "two state solution" for so long they believe it is the best outcome, but know nothing about the material conditions. - your well meaning but brainworm riddled Aunt.

The realist. Knows "two state" is bullshit. Doesn't want to reveal their power level and scare normies. Might parrot the phrase for rhetorical reasons, but understands the reality of the West Bank. - every Palestinian activist who says "two state" on a public forum, at least when cornered.

The dog of Empire. Knows "two state" is bullshit, might not consciously acknowledge it, but if pressed will admit it. Uses it to justify occupation (Palestine isn't a state yet) and as a carrot to trick people into thinking they are reasonable. "I think, two states is the best solution, but . . . ." - the US State Department, and every white man whose profile pic shows them driving a pickup truck while wearing sunglasses

In my anecdotal opinion, the ones I interact with most online are dogs of empire. Most "average" people are just ignorant. Although after funding and supporting a genocide for a year my sympathy for the ignorant has been exhausted.