Muzan didn't want you to stay on the demon's cave so he sent a message to Kagaya that you'll be staying with the Hashiras. Kagaya trusts you and he let you stay with them. Kagaya talked to the other Hashiras

Sanemi:HOLD UP!? MUZAN'S KID?!

Obanai:Are you sure master!? What if he/she attacked us!?

Shinobu:Hm..this kid really do look like Muzan.

Mitsuri:Yeah! But she/he is cute!!

Tengen:That's a problem..

The other Hashiras stayed silent and some of them are shocked