So what is the general opinion about pets like dogs and cats inside houses in Turkey? I heard Turks find it disgusting and will only keep dogs outside. 

My mother doesnt let me have cat at home. I will run away and live on the streets with them.

there are still many people who keep dogs at flats, but the neighbors report them if the dog makes sound. typical really, nothing special to turkish people. well also we love cats on streets

in my village almost in everyhouse there is a cat. they live in the house and have a private corner in one of the rooms to eat and sleep. when the doors closed they will start to meoww and immediatelly someone opens the door...

anyway, in modern families all pets are welcomed. in partially or fully religious families dont let the dogs live in the house. dogs have to live outside, in one corner of the garden or in barn.

Religious background for keeping dogs inside of a home:

Hadith - Bukhari 3:515, Narrated Abu Huraira

I heard Allah´s Apostle saying; "Angels (of Mercy) do not enter a house wherein there is a dog or a picture of a living creature (a human being or an animal)."

Hadith - Bukhari 3:515, Narrated Abu Huraira Allah´s Apostle said, "Whoever keeps a dog, one Qirat of the reward of his good deeds is deducted daily, unless the dog is used for guarding a farm or cattle."

As in everything, Islam is very compassionate and understanding. I´m sure dogs that are used as therapy, or guide dogs are welcome. 

Guide dogs Therapy Dogs

I think cats and dogs are two different things in Islam. A dog is a filthy animal which should be kept outside (but not treated in a cruel way) but I have understood there is a blessing in cats. The nickname of Abu Hurayra, one of the Prophet´s SAAS companions refers to his affection to cats. I don´t know if this means cats were kept in the houses, though. Hardly.

But I have heard some people (or people in some areas I don´t know) in Turkey are afraid especially cats or cat fur brings fatal diseases. Based on what who knows.

found on here

http://www.huffingtonpost.com/2012/09/15/islam-on-dogs-can-you-be-_n_1885580.html

The Quran mentions dogs twice, including the permission to eat meat that has been carried by hunting dogs. In another verse, a group of "believers" and their dog escape their persecutors by hiding in a cave, where they fall asleep. "And their dog stretched his forelegs across the threshold," the verse finishes.

"This tender description of the dog guarding the cave makes it clear that the animal is good company for believers," Ingrid Mattson, chair of the Islamic studies program at Huron University College, wrote last December in a column for The Huffington Post.

While many Muslims believe scripture approves canine companions, many also believe scripture discourages Muslims from keeping dogs in their homes. This belief is partly based on the Quranic verse describing the dog at the threshold of the cave, as well as a story in which the angel Gabriel breaks a rendezvous with the Prophet Muhammad because a puppy had wandered into Muhammad´s home.

"We angels do not enter a home in which there is a dog or a picture," Gabriel tells the prophet.

There are also a few hadith, or sayings attributed to Muhammad, that are hostile toward dogs, including a couple in which he orders the killings of dogs. But Islamic scholars and other Muslims say that many hadith are fabricated or hard to verify, including those about dogs. And because these hadith contradict the apparent divine sanction for dogs in the Quran, these stories should not be trusted.

As you said Islam considers dog as a filthy animal and I should mention Islam really gives big importance to hygiene.

If you dont pay attention to hygiene you will be even punished for it:

He should be careful to remove all impurity after answering the call of nature, because the Prophet (peace and blessings of Allaah be upon him) warned against being careless in cleaning oneself after urinating: “Most of the punishment of the grave will be because of urine.” (Reported by Ibn Maajah, 342; see also Saheeh al-Jaami’, 1202). Ibn ‘Abbaas (may Allaah be pleased with them both) reported that the Messenger of Allaah (peace and blessings of Allaah be upon him) passed by two graves, and said: “They are being punished, but they are not being punished for any major sin. One of them used not to protect himself (i.e. keep himself clean from) his urine, and the other used to walk about spreading malicious gossip.” (Reported by al-Bukhaari, 5592).

.... example: “the stories of Muezza, the Prophet Muhammad’s SAWA favourite cat: The most famous story about Muezza recounts how the call to prayer was given, and as Prophet Mohammed SAWA went to put on one of his robes, he found his cat sleeping on one of the sleeves. Rather than disturbing the cat, he cut off the sleeve and let him sleep. When he returned, Muezza awoke and bowed down to Prophet Muhammad SAWA and in return he stroked him three times. It is also believed that when Prophet MuhammadSAWA gave sermons within his household he would often hold Muezza in his lap”.

"It is related that after the death of the great Sufi Master al-Shibli, a friend saw him in a dream. The friend asked him what God had done with him, to which al-Shibli replied, “God placed me before Him and asked if I knew why He had forgiven my sins. I said that it might be because of the good works I had done, the prayers I had performed, my fasting and pilgrimage, my having associated with pious people and my journeying in search of knowledge. God replied, “O Shibli, these were not the reasons. Do you remember when you were walking in the lanes of Baghdad and you found a small cat made weak by the cold and ice, and out of pity you took it and put in inside a fur you were wearing so as to protect it from the pains of the cold? Because of the mercy you showed that cat, I have had mercy on you.”