Is it allowed to buy cats with money in Islam?

It is not harram. In Shi'a Islam if you have a cat in your house it shouldn't enter a prayer room or sit or touch your prayer mat or prayer cloths because the hair of the cat is 'najiss' (impure). Also a dog is najiss, its not harram to keep one but it will corrupt your salah (prayer), your prayer wouldnt be accepted, that also refers to cats.

However according to Sunni islam, cats and cat hair is not najis at all. You can keep a cat in your house. It is just how you obtain one that is being discussed, ie you can adopt one but not buy it for profit. The prophet (s) did not elaborate on why this is. This means that even if there was cat hair on your clothes or the cat licked you, your prayer would still be accepted. The prophet (s) did his ablution from the same water that a cat had drunk from. However if the cat has a visible najasa in her mouth, like a mouse then you should wait a little while after this has been removed and her saliva is tahir (clean) again.

However in sunni islam a dogs saliva is always najis although their hair is tahir as the hadith tells us. One cannot keep a dog for entertainment purposes at all. The only dogs that can be kept are hunting, guarding or herding dogs and even then they must not enter the house. If you keep a dog for entertainment purposes, your good deeds will be reduced by one to two qiraat everyday.