First up, I am a cat lover and have two of my own who are indoor cats with an outdoor run and harness trained for walks; this is for their safety and that of the wildlife.
Being a cat lover does not stop me getting extremely angry about other people’s cats wandering and terrorizing the neighbourhood.
Possibly coincidentally, I lost a happy, healthy, less than 2 year old chicken on the night of a cat fight which happened right next to the coop; lots of hissing and screaming etc. I went out the next morning to find KiKi dead on the coop floor. While I can not prove it, I suspect she died of fright or fell off the roost from fright etc.
I have another story where one of my cats, who never tries to dash out the door, did so one day because she saw across the roads' cat under our car in our carport .. she chased him back to his house, across the road, stopped and realised where she was [outside and unknown territory] and turned around, running back across the road towards me and in front of an oncoming car .. I nearly watched my beautiful girl get run over and I am so grateful that the driver either saw her in time or me having a hissy fit on the side of the road and swerved to miss her.
If their cat had remained on their property and not encroached on to ours, she would not have dashed out the door.
I have no idea how I stopped myself from walking across the road, ringing their door bell and punching them in the nose! LOL
I will climb down off my soap box now because I could rant and rave for hours about irresponsible cat owners, but I recommend going over to your neighbours, telling them that you have chickens on your property and that you would like them to not allow their cat to wander on to your property.
Yes, you did hit a nerve

LOL