Ideologically means based on a set of beliefs. When you say that someone is ideologically opposed to something, you mean that they hold a very strong opinion against it.
He is ideologically opposed to abortion, which is why he is against it.
The politician is ideologically opposed to the government, which is why he is protesting.
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The ideology they promote is an oxymoron.
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Her ideology was somewhat labile.
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Christians should transcend ideology.
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The essay establishes the concept of ideology.
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The ideology and the political movement are inseparable.
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The ideology of the group was Irish nationalism.
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The ideology of the party was strongly secular.
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They are hostile to the political ideologies of the PQ.
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This is the article on the ideology and the political movement.
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A third reason is to promote the ideology of the broadcaster.