Can card abilities be interrupted/reacted to like spells, and what types of abilities cannot be disrupted?

Ruling: Yes, most card abilities go on the stack and can be reacted to by opponents. Only Passive abilities and Replacement Effects (like Legion tags, Zhonya's Hourglass, etc.) cannot be reacted to. Permanents and Add abilities also cannot be reacted to.

Sequence:

• When an activated or triggered ability is used, it goes on the stack
• Target must be announced when the ability is activated
• Opponents can respond with reactions before the ability resolves
• If the target is moved off the battlefield before resolution, the ability resolves but does nothing
• If the source of an activated ability is moved, the ability still resolves (only needs to be valid at activation)

Nuances:

• Playing a card itself (the permanent entering play) cannot be reacted to, but triggered abilities from that card (like "Here" effects) can be reacted to
• Ability types: Passive, Replacement, Activated, Triggered, and Delayed - only Passives and Replacements cannot be reacted to
• Moving the source of an activated ability back to base does not stop it from resolving
• Moving the target of an ability causes it to resolve without effect