Parents don't like my relationship

[Kernel]

well iv been goin out wif my girlfriend for more than a year now and our parents have been fine with us going out. but recently they haven't. For no reason at all, our siblings have been sayin that us hugging/cuddling is wrong. . and our parents don't allow us to have any time alone. I feel like they dont trust us but we've done nothing wrong like that. Honest

So wat do i do? cause i'm lost here. . its horrible. How can i get them 2 trust us again and let us be alone even for a while??

[Clawhammer]

Work at your family relationships. Earn that trust and talk to them. Have you been avoiding other things you should be doing to be with your girlfriend? Is your relationship having any negative effects on anyone? It may or may not be something that you need to work at too. Maybe don't make it look like you constantly want to be alone with her? You could see if there's any way to "bring things out into the open," and take it easier on physical contact around the family?
Just some thoughts. Just work at showing them you can manage things and be trustworthy, but don't expect immediate results.

[FreeFall]

Your family seems to have an issue with PDA. My bf's family's like this, no kissing on the cheek or we get yelled at. We can only hold hands when there, our legs can't be touching when we sit next to each other, nor can I so much as rest my hand on his shoulder.

So you have to earn their trust back and stop with the touching in their presence. You sound like you've got younger siblings yes? the parents are probably concerned that them seeing you cuddle and hug and constantly touch each other, will impression them to be very touchy feely in their relationships. if they're older siblings, they've probably voiced concerns of you two being promiscuous.
They're the parents though, their rules. Some people aren't allowed to be alone with their significant other so long as they live under their parents roof, even if they're adults.