Indra is highly extolled in Vedas. From various stories, including Brahmana we find his various illicit relationships with other's wife. These stories make me to think why Vedas or scriptures giving respect to him? Or why he should be worshipped? Do any scriptures explain why we should accept him even after knowing his deeds?
Indra should be worshipped because the Vedas ask us to worship him. That is reason enough. What more reasons do you want?
The Vedas, not only praise Indra as worship-worthy, but also ask us to make him the exclusive object of our worship.
Indram vo vishvatah pari,
AsmAkam astu kevalah ||
Indra, standing above all, is called by the seekers. May he be the exclusive object of our worship.
Rig Veda 1.7.10
And, why only Indra, even Agni, who is the chief among Vedic Gods, is also described as having committed illicit crimes, as did Indra. And, we find the stories in the Vedas themselves.
The waters were the wives of Varuna; Agni longed for them, he had union with them; his seed fell away, it became this (earth); what second fell away became yonder (sky); this is the Viraj, yonder the Svaraj; in that he puts down two Viraj (bricks) he puts down these two (worlds).
Yajur Veda Book5, Part5.
But, Agni is still considered as the foremost among all the PAvamanas (purifying principles) of the Vedas.
And, for him we have such verses as given below:
Agnim dutam vrnimahe, hotAram vishva vedasam, Asya yajnAsya sukratum ||
We choose Agni, the all-knower who, as our envoy, invites the Gods. He is the auspicious performer of yajna.
Rig Veda 1.12.1
Agnir murdhA divah kakut, patih prthivyA ||
Agni is the Head and Peak of Heaven and the Lord of this Earth.
Rig Veda 8.44.16
So, Vedas, themselves say that Agni committed such and such crimes, but yet they mention him as supremely worship-worthy. So, so be it. That is reason enough why Indra, Agni etc are to be worshipped.
It's important to remember many hindu scriptures tend to be highly metaphorical. Ancient sages used stories as instruments to convey a moral story.
It can be argued that the word 'indra' is widely understood as 1) king of gods in heaven 2) the senses of the body (viz eyes, ears etc)
Now "indra chasing other's wives" could also be interpreted as an ordinary man's affairs with others women because his sense inspire him so .
Indra being extolled could also be understood as human senses being extolled . These sense , while they can be used to do bad, such as chasing other's wives, can also be used for productive purposes, including spiritual reasons. Hence the extollation
Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.