Cat behaving oddly with another cat

[Friday1234]

We have a young male (neutered) cat who likes being outside a lot. He’s what I think is appropriately territorial in our garden. He likes to be on top of the shed keeping an eye out and staring at other cats, puffing up if they get too close and hissing etc. He’s absent from the garden a lot too but no idea where he goes.
Recently another cat (who looks a lot like him weirdly) has been taking up his spot on the shed and our cat doesn’t seem at all bothered. He’s just slinking around - no puffing and happy to have his back to him. It’s very out of character, which is concerning me a bit. But what’s also very annoying is that this other cat keeps coming in our house, eating our cats food, heading upstairs etc. I’m worried that this isn’t a great situation for our cat. Plus cat food is expensive. We don’t have a cat flap - we have the back doors open because of the weather. I’m reluctant to get a cat flap and keep the doors closed because I like fresh air and we have no obvious place for a cat flap so would have get one installed in the wall. I could probably suck up the cost of that but not straight away.
I guess I’m asking if there is a way I haven’t thought of to keep this cat away? (Currently using a water pistol but I’m not on look out 24/7).
Is another cat coming in likely to be stressful for my cat?
And, why is he behaving differently with this cat?

Maybe it's his boyfriend? Or it's more dominant than him and he's afraid to tackle it. Is your cat actually stressed or just nonchalant? How do they react when in the house together? I guess you could try and trace the owners. Put something on Facebook etc. Not sure what you can do about it though, cat's will be cat's and go where they want, lol.

We had a cat who kept coming in. Unneutered male and attacking my 2 year old girl cat. He died but now his spot has been taken by my neighbours cat who’s decided he fancies my 12 year old girl cat and keeps coming in and she hisses at him. There’s not a lot you can do.

It sounds like they’re friends? Unless your cat is showing signs of stress or fear then it sounds perfectly normal to me - many cats are quite sociable and happy to hang out with others.

When your cat is absent from the garden he might well be wandering around someone else's house, much the same as you have with the strange cat 🤷‍♀️.

As you know, the only way to control the situation is to have a cat flap or close the doors, and if you don't want to do that then you accept you're going to have a visitor. Your cat seems to be okay with this one, so probably best to be thankful for that...better than having a determined interloper who gets in a scrap with yours on a daily basis.