Do Guidance and Bardic Inspiration bonus dice stack?

Question

The feature/cantrip descriptions says nothing about their dice can not stack:

Bardic Inspiration

... use a bonus action on your turn to choose one creature other than yourself within 60 feet of you who can hear you. That creature gains one Bardic Inspiration die, a d6. Once within the next 10 minutes, the creature can roll the die and add the number rolled to one ability check, attack roll, or saving throw it makes.

Guidance

You touch one willing creature. Once before the spell ends, the target can roll a d4 and add the number rolled to one ability check of its choice.

That feels wrong to me, since a pair of 1-level characters can have ridiculously high (up to +10, +6 average) bonus to an ability check.

To my knowledge, bonuses in D&D 5e (advantage, proficiency bonus, etc.) do not stack, hence the question. Can a player use both Bardic Inspiration die AND d4 from Guidance for the same check?

I've found a related question, but it is about 3.5e.

Answer 1

Bardic Inspiration and Guidance both say "the creature can roll [the die] and add the number rolled to one ability check". Adding is adding - nothing prevents you from adding other bonuses. Bardic Inspiration only specifies the limitation of having one Bardic Inspiration die at a time.

From Jeremy Crawford, the man himself:

Do bonuses from Bardic Inspiration and Guidance stack? Can they be applied to the same roll?

Crawford: Yes.

The only reason two effects might not stack is if they are the result of the same spell cast twice, which this is not - Guidance doesnt stack with itself from two castings, for example. See "Combining Magical Effects", PHB 205.

The effects of different spells add together while their durations overlap. The effects of the same spell cast multiple times don't combine, however.

Jeremy Crawford's ruling via twitter takes this a step further, extending the above rule to apply anytime the same effects are from "game features" with the same name, ie class features (like the +1 AC from the Defense Fighting Style in a multiclassed PC), magic items, etc.

Crawford: Effects from game features with the same name never stack. #DnD