Do the Lvl 7 Champion and the Lvl 3 Thief abilities (adding str and Dex mod distance to jumps respectively) stack?

I know in most cases where a class allows you to add an ability modifier to a check it doesn't allow you to stack another one as well (I.e. gloomstalker/Swashbuckler does not add both Wis and Cha to intitiative, monk/barb does not add both Wis and con to AC).

Monk and Barbarian abilities don’t stack because the class abilities give you an alternative way to calculate your AC. You have to choose one way to calculate AC. For instance, a multiclass Monk/Barb could choose to use the monk ability. If they don a shield, they couldn’t use the Monk ability but they can still use the Barbarian ability so they can switch to that.

But do the Thief and Champion jump abilities stack?

I don't see why not. They both say they add their respective modifier to the distance of a running long jump rather than saying distance jumped = normal + modifier (like AC calculations do). So yes I would say so.

They are both bonuses, so they stack. But remember, you cant jump further than your remaining speed.

I'm not 100% on whether walking speed unambiguously remains a hard cap on distance jumped when subject to these class features RAW. It comes down to where those features insert their additional "distance you can cover": after the first clause but before the limiting clause (you can cover normal distance plus some extra, but it all costs walk speed which you can't exceed), or after the limiting clause as an additional bonus (you can cover normal distance which costs walk speed that you can't exceed, and then a few extra feet from the feature). The wording "the distance you can cover increases..." is at least open to the idea that this is bonus distance once you've exhausted the normal calculation, operating as a specific exception to the general rule. Same with Jump; I don't see that RAW the spell doesn't allow you to triple your distance and violate the normal walking speed limitation. (I am aware that Crawford has clarified a RAI limitation, I'm just saying I don't see it in the text RAW). 

To plug an alternate RAF for a moment.... The way that Chapter 8 and Chapter 9 read, it really seems like an opportunity was missed for jumping (maybe requiring a Jump action or bonus action?) to create a Jump Speed, equaling your strength score if you got a running start or half strength score otherwise. Chapter 9 is very clear about how using multiple forms of movement works: if you switch between movement modes with different values (example is from walking to flying), you deduct the distance you've already moved from the mode youre switching to. Walk 30/Fly 60, so if you walk 10 feet and then take to the air, you can fly 50 more feet. How much simpler a world we would live in if jumping gave you Speed 30 Walk/[Str or Half-Str] Jump, and that Jump speed could be freely modified by these class features, Jump, etc! Instead, we have a rule which essentially does just that, but uses unique features and terminology in such a way that makes it work wholly unlike flying, climbing, swimming, or any other known form of movement :( 

 Both increase your jump distance, your jump distance by RAW uses movement. That isn't ambiguous.

If they were meant to increase jump distance without using movement they would be worded closer to: "when you make a long jump, you can clear an additional distance equal to [value]."

I’m not sure there’s a lot of daylight between “the distance you can cover increases” and “you can clear an additional distance.”

Quote from Chicken_Champ >>

I’m not sure there’s a lot of daylight between “the distance you can cover increases” and “you can clear an additional distance.”

 Well one falls firmly within the rules for a jump, the other sort of doesn't. It was the best I could come up with without including "this distance can exceed your movement."...