My partner and I did that. Things didn't go to plan for me getting into uni, so I ended up getting a job and buying a house. He was doing a PhD. His parents arrived one weekend at my house with all my stuff!! 😂, they assumed he was moving in! ( he was but they didn't know that). A year later I went back to uni and did my degree.
Finances, we were lucky, mortgage was £150 a month to be split 50/50!!
I paid all the council tax while I was working, we had a 50% reduction for student, we didn't go 50/50 on everything, we both paid a set amount to cover the mortgage and bills equally, then what was left was our own. We still work like this now as our wages are significantly different.
We got together at 16, we are 40 now and still together! So it can work!
We didn't have any hiccups, we both had social lives separate and together, mostly together because we had the same friends.
As for parents..don't worry about them, show them that you are being financially sound by living together. It makes total sense!