A creature's magic immunity doesn't interfere with the creature's ability to use magic generally…
The Monster Manual II half-golem template on Creating a Half-golem (210) mentions nothing about removing the base creature's spell-like or supernatural special attacks or special qualities. It also doesn't mention that the base creature's spell casting is changed or removed. In fact, on Half-golem Characters says, "Those [half-golem characters] who seek revenge [on the world] generally become fighters or rogues. Those who retreat from [the world] become barbarians, rangers, or druids. A rare few become, or remain, evil clerics" (210).
Of course, this doesn't necessarily mean that after becoming a half-golem creature and potentially gaining the ability cast spells from having taken class levels in druid, cleric, or whatever that the half-golem creature can cast spells, but as there's no mention of losses—only gains—in this regard, this reader is fairly confident that creatures that possess the template half-golem can cast spells, use spell-like abilities, and use supernatural abilities.
(Also see elite opponent Slisk who, after becoming a half-golem, retains yuan-ti spell-like abilities… and continues to retain them even after becoming, later in the article, a full-on construct.)
…But magic immunity may interfere with a creature's ability to use on itself its own magical abilities
"A creature’s spell resistance never interferes with its own spells, items, or abilities," says the Dungeon Master's Guide on Spell Resistance (298), but the extraordinary ability magic immunity is not spell resistance nor is it the extraordinary ability spell immunity (Monster Manual 315).
Instead, the magic immunity ability grants "immunity to most magical and supernatural effects, except when otherwise noted" (Monster Manual 134), and whether an immunity can be raised or lowered (in much the same way spell resistance can) is the subject of some debate (see this question). (An example of a supernatural ability that is otherwise noted is the supernatural ability haste of the clay golem (134–5).)
Ask the DM if an immunity can be raised or lowered and if the DM rules that it can't, the half-golem creature must soldier on without the buff spells that help its allies.