Well, yes, Food Chain's ability is a mana source:
406 - Mana Abilities
* 406.1 - A mana ability is either (a) an activated ability that could put mana into a player's mana pool when it resolves or (b) a triggered ability that triggers from a mana ability and could produce additional mana. A mana ability can generate other effects at the same time it produces mana. [CompRules 2003/07/01]
You are correct that it is unstiflable. And they cannot respond to a goblin coming into play because you have priority. And they can respond to the CIP ability. However, they CAN disenchant the Food Chain in response to you "playing" the goblin and putting it on the stack. Which you would know if you read my Rules Jumpstation up top
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408.1 - Timing, Priority, and the Stack
* 408.1a - Spells and activated abilities can be played only at certain times and follow a set of rules for doing so. [CompRules 2003/07/01]
* 408.1b - Spells and activated abilities are played by players (if they choose) using a system of priority, while other types of abilities and effects are automatically generated by the game rules. Each time a player would get priority, all applicable state-based effects resolve first as a single event (see Rule 420, "State-Based Effects"). Then, if any new state-based effects have been generated, they resolve as a single event. This process repeats until no more applicable state-based effects are generated. Then triggered abilities are added to the stack (see Rule 410, "Handling Triggered Abilities"). These steps repeat in order until no further state-based effects or triggered abilities are generated. Then the player who would have received priority does so and may play a spell or ability, or take a special action (such as playing a land), or pass, as governed by the rules for that phase or step. [CompRules 2003/10/01]
* 408.1c - The active player gets priority at the beginning of most phases and steps, after any game actions are dealt with and abilities that trigger at the beginning of that phase or step go on the stack. No player gets priority during the untap step and players usually don't get priority during the cleanup step (see Rule 314.3). The player with priority may either play a spell or ability, take a special action, or pass. If he or she plays a spell or ability, or takes a special action, the player again receives priority; otherwise, his or her opponent receives priority. If both players pass in succession (that is, if both players pass without taking any actions in between passing), the top object on the stack resolves, then the active player receives priority. If the stack is empty when both players pass in succession, the phase or step ends and the next one begins. [CompRules 2003/10/01]
* 408.1d - A player may play a spell or activated ability only when he or she has priority. Spells other than instants can be played only during a player's main phase, when that player has priority, and only when the stack is empty. [CompRules 2003/07/01]
* 408.1e - When a spell is played, it goes on top of the stack. When an activated ability is played, it goes on top of the stack. [CompRules 2003/07/01]
* 408.1f - Triggered abilities can trigger at any time, including during the playing or resolution of a spell or another ability. However, nothing actually happens at the time the abilities trigger. Each time a player would receive priority, each ability that has triggered is put on the stack (if it hasn't already been put on the stack). Then the player gets priority and may play spells or abilities. (See Rule 410, "Handling Triggered Abilities.") [CompRules 2003/07/01]
* 408.1g - Combat damage goes on the stack once it's been assigned. For more information, see Rule 310, "Combat Damage Step." [CompRules 2003/07/01]
* 408.1h - Static abilities aren't played-they continuously affect the game. Priority doesn't apply to them. (See Rule 405, "Static Abilities," Rule 418, "Continuous Effects," and Rule 419, "Replacement and Prevention Effects.") [CompRules 2003/07/01]
* 408.1i - Special actions don't use the stack. The special actions are playing a land (see Rule 408.2d), turning a face-down creature face up (see Rule 408.2h), ending continuous effects or preventing delayed triggered abilities (see Rule 408.2i), and suspending or ignoring continuous effects (see Rule 408.2j). [CompRules 2003/12/01]
