But they liked a bunch of my Instagram photos!
Oh boy, then imagine how badly they must want to date small kittens, seafood platters, and racist memes. Maybe if they had to send likes by snail mail this might provide some valuable insight. While such a gesture can be indicative of some attraction (now that double-tapping has effectively replaced breathing), this effectively means little more than, "I haven’t filed a restraining order... yet."
But they told their parents about me!
My mother and grandmother once heard me have sex with a girl not only before meeting her, but without meeting her (we were living in disturbingly close quarters at the time). The following day, I told them about the girl. After that, I did not date the girl. Sometimes parents and children are close. "Friends" close. Perhaps, too close. Just because mommy or daddy knows you exist, it does not mean that existence is a particularly meaningful one. Being invited to meet extended family? That's a different (horror) story.
But they're not even pushing sex, they just really want to spend time together!
Considering that sex is one of the only things people like more than puppies, this means your situation could be going either way. It could be that they're bonding with you at an advanced level. Or, they really like you and are trying to mitigate potential complications or distractions that can arise from unmitigated boning. Or, something you or someone else did has called into question your sex appeal and romantic future... thus forcing them to slowly relieve your genitals of all active duty. They could also just be super boring.