intrusive has no recorded synonym. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its 3 recorded opposites are unintrusive, extrusive, protrusive.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
tending to intrude (especially upon privacy)
“she felt her presence there was intrusive”
of rock material; forced while molten into cracks between layers of other rock
thrusting inward
“an intrusive arm of the sea”
Synonyms, antonyms and the broader and narrower relations for intrusive come from Princeton University’s WordNet. Full sources and licences.