Neil would be 100% confused, that doesn't mean against it. He'll probably start using the condoms again.
Pete and Monica love Josy, we find that out in EP5. I think so that both of them, like Neil, would be confused at first. But if they see to make Josy happy, then they won't put Pete and Monica in the way of the three of them. I tend to see Iris Moore and Clive as a problem, but they don't have much to report to Josy.
Patrick will definitely be against the throuple. Nothing can be written about Helen because she is still the big unknown.
But by and large, the parents don't play a big role. Josy's school fees have already been transferred and the MC is taking out a student loan. If Maya gets out of the contract with the help of Royce's attorney, she can also take out a student loan. With that, all three are independent from their parents and the throuple can be made official.