My Saluki is a model of decorum. He has never rolled in anything unspeakable since I have owned him. I have had him nearly 5 years and he is nearly 14. He is very posh and knows it, sometimes he will deign to be fussed by a stranger but mostly not. Very aloof. I have never known Salukis roll in poo, your Mum must have had an odd one.
Gabriel, the Saluki doesn't like cats though, or rather he does but is not fussed which meal he has one for.
They're a wide range of styles so maybe some are more keen on it than others, luckily Max, our fecal magnet, is short haired so it comes off pretty easily but he is a sod for finding the worst smelling and wettest lumps of the stuff he can.
also luckily (metphorically speaking) he's got a hefty ankle problem at the moment so is only walking on his lead & doesn't need a shower or play under the hose twice a day right now.
as for cats in the garden, I've not found anything that works from lion poo to those green jelly pellets etc, we jusrt have to slip the latch on the back door and the promise of 2 greyhounds and said Saluki pelting out to say hello seems to work.
We need a dog flap for the day though but don't want the break in risk. Whilst cats would get a pasting, they're that keen on people they'd be helping them out with the telly just for a pat on the head.