Rahu and Ketu are part of a demon who fraudulently became immortal. But why respect them and do their pradikshna in temple? I am looking for an answer which says more then “to avoid negative influence from Rahu and Ketu they should be worshipped”?
Because the scriptures ask us to worship them. That's why they are worthy of worship.
There is a detailed chapter (called Graha Shanti) in Yajnavalkya Smriti dedicated to Navagraha worship.
Verses from that chapter are given below:
CCXCV.—A person desirous of Sri or good fortune, or desirous of S^anti or propitiation should perform Graha Yajna (sacrifice to the planets). So also a person desirous of rain, long life and health. Similarly if he desires to perform sorcery also.—295. (Chapter 12)
So, the above are some reasons why one should worship Rahu, Ketu and the other Grahas.
Surya (The sun), Soma (the moon), Mahiputra (the son of the earth, Mars), Somaputra (the son of the moon. Mercury), Brihaspati (Jupiter), Sukra (Venus), Sanaichara (Saturn), Rahu (the ascending node) and Ketu (the descending node), these are remembered as Grahas.—296
Next the text gives the details of performing the Yajna/Puja. Like how to invoke them, what Samidhs, Mantras are to be used for each of them etc.
The fire-stick for the sun should be of Arka, for the moon Palasa, for the Mars Khadira, for the Mercury Apamarga, for the Jupiter Peepal, for the Venus Udumbara, for the Saturn S^ami, for the Rahu Durva, for the Ketu Kusa. These should respectively be the Samidhs for the respective planets.
Also, the primary reason we worship the Grahas, whether it is Rahu/Ketu or any other, is getting rid of their malefic effects. Because Navagrahas can not be Ishta Devatas.
Moreover, according to a boon given by Lord Brahma, the Navagrahas must worship those who worship them.
Whenever a planet has a bad aspect (in the horoscope of a person), that person should worship with great care specially that particular good planet. For Brahma has given this boon to them *' Being honoured you will honour him/'—307.
And, especially the kings of the states are particularly advised to appease the Navagrahas because they responsible for both the origin and destruction of the world. Because they control our destiny/fate.
By lords of men should be worshipped with greatest care the planets because the rise and fall of monarchs is dependent upon the planets, so also the origin and destruction of the worlds.—308.
Similarly, the Matsya Purana also details of how Navagraha Shanti is performed:
Karaala vadanah Khadgacharma Shuli Varapradah,
Neela simhaasanascha Rahuratra Prashasyatey/
( Rahu Deva is fierce looking, carries sword, skin sheath, Shula and Vara Prada by his four hands and is seated on a blue throne).
Dhumraa Dwibaahavah Sarvey Gadino vikrutaananah,
Grudhraasana gataa nithyam Ketavah Syurvara pradaah/
(Ketu Deva is of grey colour and of fierce Rupa with two hands showing gadaa and varada mudra seated always on a vulture)
Sarvey kireetinah kaaryaa Grahaa Lokahitaavahaah,
Hyaanguleynocchritaah Sarvey shatamashtottaram sadaa/
(These are all beneficient Grahas worthy of ornamentation with Kiritas/head gears and be of hundred eight inches of Pratimas / Idols).
So, the scriptures themselves mention them as worthy of worship. And, in matters like religion, scriptures are our primary guide without which we can not do much on our own.
Also, note that prior to the Mohini episode, when Rahu and Ketu were not separated (by Lord Vishnu), the Asura was not worship-worthy. It's only after the head and the body of the Asura were separated they were included into the Navagraha group and regarded as worthy of worship.
You shouldn't judge someone from their past deeds all the time. You should see their present deeds too. Whatever he (Rahu/ketu) did in past, he already got punishment of that sin. After getting punishment, person becomes sinless. And we can't call him sinful anymore. Following shloka explans this..
राजभिः धृत दण्डाः च कृत्वा पापानि मानवाः |
निर्मलाः स्वर्गम् आयान्ति सन्तः सुकृतिनो यथा || ४-१८-३१
maanavaaH = humans; paapaani kR^itvaa = sins, on making; raajabhiH dhR^ita daNDaaH ca = by kings, imposed, punishment, also; nirmalaaH sukR^itinaH santaH yathaa = unblemished - sinless, with good deeds, pious souled ones, as with; svargam aayaanti = to heaven, they come.
When kings impose proper punishment on the humans who have sinned, they become sinless and enter heaven as with the pious souls with good deeds.' So says one verse of Manu.
Following shloka explains, if one got punishment then he becomes pure or sinless. Since Rahu/Ketu got Punishment by Lord Vishnu himself then he is now fully pure. He is no more sinful person. This is the reason we should not consider him a sinful person anymore.
Why worship, respect and do pradikshna for Rahu and Ketu?
Because they are two of the 9 grahas. And all Grahas plays important roles in everyone's life. Graha's movement pattern decides what will happen in our future. And all 9 Graha worthy of worshiped. In Hinduism, we even have separate Puja for all 9 Grahas called as "Nava Graha Puja". In Sri Kala Hasti temple, there is a special pooja performed for Rahu and Ketu for decreasing astrological effects. This is the only temple where Rahu and Ketu are worshipped during eclipse and other temples are closed.
There are many benefits also which we can get by worshiping Grahas. There are some Graha which can give you grief like Shani, Rahu, Ketu etc. (because of your some bad deeds). But by worshiping those Graha, you can decrease impact of those grief or you can even remove it completely. All Grahas are like devas who plays important role in continuity of life that's why they are worthy of worshiping. Rahu and ketu also performing his divine duty like all other Devas and Grahas, that's why Rahu and ketu are also worship-able.
According to Nava Graha Stotram, Rahu and Ketu gives attractive nature and fulfills our desires respectively:
Let the Sun give me all prosperity, the Moon excellent fame, Angaraka valour, Budha wisdom, Guru long life, Sukra kingdom, Shani victory, Rahu attractive nature and Ketu all desires.Let all the planets give me support.
Actually post is worshiped and sometimes the post can be given to Asuras too.
For an instance, as discussed in
Bali Maharaj (a daitya) will hold the title of Indra (yes Indra is a post, Purandara is mentioned as Indra of 7th/current Manavantara) in 8th/next Manavantara by the grace of Lord Vishnu.
Though Rahu and Ketu are part of a demon who fraudulently became immortal but the matter was resolved at the end. And as per Bhāgavata Purāṇa: Skandha 8: Chapter 9,
Lord Brahmā accepted Rāhu as one of the Grahas.
And all Navagrahas are worthy of worship. In fact, as per Garuda Purana
Describing the significance of worshipping Navgraha, Lord Vishnu told Rudra --'One who worships the Navgraha with appropriate rituals attains all the four 'purusharth' (objectives of man's life).'