Can you activate a mana ability while the stack is non-empty without receiving priority?

Mana abilities are a special category of activated abilities that do not use the stack and do not require their controller to have priority in order to activate them. This is codified in CR 605.3a, which states that a player may activate a mana ability whenever they have priority, whenever they are paying a cost that requires mana, or whenever a rule or effect asks them to produce mana.

The key practical consequence is that when you are in the middle of casting a spell or activating an ability and need to pay its mana cost, you can tap lands or use other mana abilities to generate the required mana — even though the stack may already have spells or abilities on it, and even though you do not formally 'have priority' at that precise moment of payment (CR 601.2h, 605.3a).

Mana abilities themselves do not go on the stack (CR 605.3b), so they resolve immediately upon activation. This means no player can respond to a mana ability the way they could respond to a normal activated ability.

Concrete example: Your opponent casts Lightning Bolt targeting your creature, and it goes on the stack. You want to cast Counterspell in response. When you announce Counterspell and need to pay {U}{U}, you tap two Islands to produce the mana — even though the stack is non-empty and you are mid-payment. Those tap abilities are mana abilities, so they work immediately without needing priority and without going on the stack.

Note that not every ability that produces mana is a mana ability. If an ability has a target or triggers off something, it may be a regular ability that does use the stack (CR 605.1a). Always check whether the ability meets the definition of a mana ability before assuming it bypasses priority rules.