Simba, as a lion, eats the other animals of the pride lands but they still respect him.
I understand it's the circle of life, but what is the explanation in this story? If lions eat warthogs, will Pumba and Simba continue to be friends?
Simba gets respect from pride lands animals but why?
One of the things Mufasa was trying to teach Simba when he was young was about the delicate balance in nature.
Mufasa: Everything you see exists together, in a delicate balance. As king, you need to understand that balance, and respect all the creatures-- from the crawling ant to the leaping antelope.
Simba: But, Dad, don't we eat the antelope?
Mufasa: Yes, Simba, but let me explain. When we die, our bodies become the grass. And the antelope eat the grass. And so we are all connected in the great Circle of Life.
The Lions (who follow Mufasa) here aren't just carnivorous that hunt and eat everything in the Pride Lands, they respect the other animals there. In Mufasa's understanding of nature he sees how that while the Lions are the apex predators in the Pride Lands, they also end up giving back to the other animals (assuming they are all herbivores) in the form of plants. When a Lion dies their dead body helps the Pride Lands have plants for the other animals.
We see this balance broken when Scar takes over, forcing the Lionesses to hunt for him and the Hyenas with little regard for the balance to the point where the other animals flee (they are not being respected by Scar and the Hyenas who just want to eat everything) and there is nothing left to hunt, resulting in the Pride Lands being barren and almost devoid of vegetation.
Also notice before Simba's return everything was dark but after Scar was defeated the Pride Lands light up again and the animals, symbolizing that Simba would restore and uphold the balance Mufasa did.
Lion eats warthogs, will Pumba still be friends?
While he was away from the Pride Lands Simba was raised by Timon and Pumbaa teaching him how to eat bugs. While I don't know of the time frame I would assume it was years so there is a special bond that's formed between Simba, Timon and Pumbaa and that entire time Simba has been able to live off bugs.
We also see this bond when Nala is stalking Pumbaa and goes to hunt him for Scar. When cornered Simba appears and fights off Nala. While not realizing it was Nala it shows that Simba would fight any Lion if they attacked his friends. As such even as King I don't think Simba would allow his friends (who even helped fight the Hyenas) wind up on the dinner plate.
To further the other answer and to then include The Lion King 1 1/2, The Lion King II, and The Lion Guard...
When we look back at The Lion King and how Mufasa sees "the circle of life" and/or what he believes to be the correct place of The Lions in nature, you have to consider that these beliefs go beyond the natural explanations (i.e.: Lions becoming part of pride lands once their bodies decay), but also because this goes into the metaphysical and there may be supernatural "consequences" for not following the universal macrocosmic order and most of the other animals must then also believe in this philosophy, in order for it to be mutual and respected.
Essentially, The Lion King Franchise has an ongoing mythology, that includes the idea that there are both good and bad consequences coming from the beyond, including "spirits of the dead" (i.e.: Mufasa in The Lion King motivates Simba to do "the right thing"), that help further motivate what the characters are taught to believe.
In that respect, besides being a cartoon, The Lion King is much more morally psychological in nature where it is often the apex predator that has to look into themselves and grow from life's experiences. (Perhaps a metaphor for wealth and entitlement and how to be "good" when you have power and need to maintain power) I have only seen a few episodes of The Lion Guard, and do not know if they ever wrote an episode geared more towards the other animals' (Kion's friends) needs or beliefs to help counter balance the narrative, but I do think it is clear that this is suppose be about finding balance in an imperfect situation or not ideal by "some" philosophical standards (Lions eating meat) without being completely false (i.e.: make all lions vegetarian), which would also then result in other untruths (i.e.: what if there weren't Lions eating other animals? How would this effect the echo system? Or if not Lions, then some other species become "apex predator" and would still face the same problem).
So sure, although in reality one might think that if animals were intelligent enough to understand philosophical ideals of respect, one still might think that most animals would completely "fear" the Lions and the Lions could not be "friends" with many of the other animals, but in the same breath, if many of the animals are that consciously evolved, and on top of it, experience things from the beyond, then why couldn't they find middle ground and accept their "fates"? This is about "religion" and spiritual philosophy, not just naturalism.
Reading through the plots of the sequel TV series, The Lion Guard there are plots that explain that the role of The Lion Guard(s) are to uphold "The Circle of Life" by protecting animals that respect it from those that do not.
Kion is the son of King Simba and Queen Nala, the younger brother of Kiara and the prince of the Pride Lands. As the second-born of the Lion King, he is gifted with a power called the Roar of the Elders and becomes the leader of the Lion Guard, a team of animals who protect the Pride Lands and defend the Circle of Life. Kion, along with his friends Bunga the honey badger, Beshte the hippopotamus, Fuli the cheetah and Ono the egret, sets out to keep the Pride Lands safe and protected from animals who do not respect the Circle of Life.
Reading through second season plots, which also somewhat ties into some of the plots during the earlier time period of the second film The Lion King: Simba's Pride, Kion, who often talks to the spirit of Mufasa, accidentally calls back the spirit of Scar who rallies the lions and animals banished from the Pride Lands, in an effort to take it away from Simba and his family.
By the end of The Rise of Scar, Kion unknowingly summons Scar back as a fiery spirit in the Outlands' volcano after he uses the Roar in anger when Janja provokes him. In "Let Sleeping Crocs Lie," Scar takes in Kiburi's float and announces his plans to unite all the animals in the Outlands to takeover the Pride Lands and defeat the new Lion Guard and Simba, who were unaware that Scar had returned. In "Divide and Conquer", Kion briefly witnesses Scar's spirit in the flames of a fire before it vanishes, but is unsure of what to make of it. Only a strange scorch mark remains, which Rafiki recognizes as a sign of terrible evil. In the following episode "The Scorpion's Sting", Scar reveals himself to the Lion Guard while they are in the Outlands collecting volcanic ash needed to cure Simba from a scorpion sting.
This just helps establish what I was trying to explain above about The Lion King having some kind of moral philosophy in terms of how they treat animals vs the need to eat.