I didn't watch it very often when it was originally on back when TLK first came out, and like most of the people here, I would have preferred it if it focused more on the main cast. However, since Timon and Pumbaa were responsible for most of the movie's slapstick, gross-out humor and human-like behavior (especially Timon, who carries a leaf full of bugs like a waiter with a tray, wears a grass skirt and makes references to things particular to the human world ["Ooh, the little cream-filled kind!"]) and antics that occasionally seem to warp reality (Timon seems to produce a skirt made of grass, a flower and an apple for their "Luau!" act despite being in the middle of the barren Pride Lands), in a way it made sense that a series focused on them would feature a lot of these elements (even if they did crank them up past 11). I never really understood Timon and Pumbaa's popularity, though. There must have been a really, really big population of really young kids that were begging their parents for T&P-themed merchandise both when TLK was first released (they never appealed to me, and I was 10 at the time).
I never attempted to try to fit any of the stories in the continuity of the films, because to me they just seemed like an irreverent, light-hearted spinoff which was never meant to be taken seriously. Still, despite their insane adventures, Timon and Pumbaa do seem to stay in character (at least, in the few episodes I've seen), and I did chuckle at some of the dialogue.
Side note: Simba and Nala's cub appears in one episode ("The Man from J.U.N.G.L.E."), and despite seeing dozens and dozens of variants of Simba and Nala's offspring where the multiple alternate names of their children are all given seperate identities, I don't think I've ever seen one cub with this particular cub's design, which just goes to show how far off most fans' radar the show has fallen:

EDIT: I messed up. This cub is never actually referred to as Simba and Nala's cub; I just assumed it was theirs since the series is set after the events of the first film and Timon knows what Pride Rock is and that the cub is going to be presented there.
(Also: If any fans are seriously afraid that
The Lion Guard is going to ruin the TLK franchise, they
really need to watch a few episodes of
The Lion King's Timon and Pumbaa. If the TLK franchise can remain largely untarnished after
that TV series, surely it can survive whatever this new one may bring.)