YANBU at all!
In this day and age, it is not weird at all for a 27 year old to still be living with parents, especially if it's in an expensive city i.e. London/SE
Yes, a 27 year old could be living independently, spending an extortionate amount of their salary on rent but yet only being able to save very little each month towards a deposit for their own place.
In the short term, yes, they are all "grown up" and independent, but in the longer term, they are going to struggle massively to raise a deposit to buy a home. (unless they earn a massive salary/are set to inherit £££)
It's hard when your family dont support your plans or question everything that you do, but you need to do the best thing for yourself and partner.
Maybe with your sister, it's more because she would like to be living with you in the near future and so does not like the idea of you moving away/in with someone else?
With respect, her opinions are likely to be strongly influenced by her current set up at university- which is often never a true reflection on real life i.e. when you need to start earning a living, paying all the bills etc and not relying on a student/parental handouts.
For what it's worth, I imagine my parents would be exactly the same as yours if I had proposed the same move aged 24 (or even now to be honest, at the age of 39!)
My parents would definitely be totally insulted, ashamed at my arrogance for "choosing" another/better family to live with.
As others have said, moving into parents with a partner will likely be very challenging indeed, even with the most solid of relationships.
I think it's really important to have an end date/goal in sight e.g. finding a property to buy by the end of 12 months (or even sooner if finances allow).
The worst sort of scenario is where you get too comfortable and end up spending the extra cash you have e.g. holidays, little luxuries that add up. Life may have to be put on hold for a bit, but if this can be for minimum amount of time, all the better.
Good luck with everything 