Below you will find 6 very potent statements by Srila Prabhupada regarding the keeping of dogs and cats in ones home or in his/her life. Some devotee still we find are keeping cats/dogs at their homes along with Deities of Lord Krsna.

I heard from one such devotee recently that she finally (after some 40 years) realized it was unclean to keep her dogs in her house along with her deities.

After how many years, it took to realize this simple concept? These things are going on, and when you point them out, you become– their enemy……

When you look at the picture above with the dog urinating on a tree with a sign that says no dogs allowed, it "should" make perfectly clear why these animals are not allowed according to Vedic civilization in such close proximity as human beings.

1) SB 7.14.11 Purport 

Although in modern society the dog is accepted as part of one's household paraphernalia, in the Vedic system of household life the dog is untouchable; as mentioned here, a dog may be maintained with proper food, but it cannot be allowed to enter one's house, what to speak of the bedroom. Outcastes or untouchable candalas should also be provided with the necessities for life. The word used in this connection is yatha, which means "as much as deserved." The outcastes should not be given money with which to indulge in more than they need, for otherwise they will misuse it.

(Note It is interesting that Prabhupada above includes the outcastes or untouchables in the same category as dogs-they can be fed, but are not allowed inside the house or close quarters with cleaner human beings-namely the 4 varnas and ashrmas.)

2) SB.1.8.29 Lecture Mayapur, Oct 9, 1974          
Canakya Pandita says, candala-vesmani. Candala means untouchable, the dog-eaters. In the Vedic conception, the dog-eaters are untouchable. Actually they should be untouchable. Meat-eaters are untouchable.

 (Note – This means when a devotee comes in close physical contact with meat eaters, they should  not be allowed to touch your feet and to take bath immediately following any physical contact-this is not fanaticism, but common sense if you want to remain clean)

3)   SB.2.9.14. Lecture Melbourne, April 13, 1972          
Surabhir abhipalayantam. Here you have got a hobby to keep dogs, "gow, gow, gow!" And Krsna has no hobby? He has got hobby, to keep cows.Surabhir abhipalayantam. You have imitated that hobby, and instead of keeping cows, they are keeping, "how!, how!," dogs. That is your capability, a nonsense which is untouchable. Dog is untouchable according to Vedic literature, and they are being kept. And cows? Killed. And cruelty to animals means not to be cruel to the cats Not cats. Yes, cats and dogs. And for the cows, "Oh, there is no question of cruelty. He has no soul. Kill him." This is your civilization, Dog civilization. You see? You keep dogs, "gow! gow! gow!", and if somebody comes to your home, to your country, you also make "gow! gow! gow! Why you have come?" Immigration department. "Please go out. Please go out." This is civilization.

4) Room Conversation Johannesburg, Oct 15, 1975 
Prabhupada: Syphilis. In Ayur-Vedic it is called phairanga, means this disease is imported from Western countries. Every dog has syphilis, and they contaminate the woman, and that is distributed to man. According to Vedic civilization, dog is untouchable. Now in India also, to keep a dog is aristocracy. Yes. Especially the tail cut. Now half-cut tail, that is aristocratic dog. Now they are making dog show in New Delhi.

5) Morning Walk Melbourne, April 21, 1976
Devotee (1): Prabhupada, last night you were describing how people serve their dogs. And now, in the Western countries, they have restaurants where you can take your dog, and he sits at the table with you and they serve a meal for him. And they have catering services. You can call up, and they will bring a special meal to your dog, so he can eat at his home. They have beauty parlors for dogs, everything.
Prabhupada: Yes, they have taken dogs as God. According to Vedic civilization, dog is untouchable. (break)

6) Conversation on Train to Allahabad India, January 11, 1977
Prabhupada: Yes. We are brainwashing from bad to good. That is our business. We are washing the brain from all rascaldom. That is our business. You are… Your brain is filled up with all rubbish things: meat-eating and illicit sex, gambling. So we are washing them.
Ceto-darpana-marjanam. Srnvatam sva-kathah krsnah punya-sravana-kirtanah, hrdy antah-stho abhadrani. Abhadrani washing. Abhadrani means bad things. The bad things should be washed off.

Don't you cleanse your home? Don't you cleanse your room? Is not that brainwashing? So if you wash your room very cleansed, who blames you? But you are so rascal that "Why you are washing this garbage?" you are protesting. You are such an intelligent man. We are washing the garbage; you are protesting, "Why you are washing the garbage?" This is your intelligence. But intelligent men wash the garbage. That is the law of nature, cleanse. That we are doing.

According to Vedic civilization, you are actually untouchable. Now we have come to touch you; therefore wash you must first. You are untouchable. In Indian civilization, dog is untouchable, and that is your best friend. So you are not touchable. Therefore we have to wash you. And unless your brain is washed, you cannot understand Krsna. So it is necessary. Is that all right? Dog is your best friend. In India dog is untouchable.

So "Man is known by his company." If your best friend is dog, then what you are? We can understand your position because you sleep with dog, you eat with dog, your best friend is dog, so what you are? You must be washed. It is a fact. Every woman, every man, has some dog.

Jagadisa: Dog or cat.
Prabhupada: Mostly dog. So "Man is known by his company." Your constant company is dog, so what you are? These are the way. Actually, according to Vedic… Why they do not allow Europeans in the Jagannatha temple? Because they are untouchable. According to Vedic civilization, Europeans are untouchable. Muslims and…, untouchable.

Not only foreigners, even in their own country, those who are not very cleansed, they are untouchable. Another's eatable things, they're untouchable. Just like hog. If you give him halava, he will not take it. He will eat stool. Therefore hog is so abominable.