Can a card that has an "effects don't affect" effect be given an effect?
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Yes, it can. It won't be affected by it, but it can be given an effect. However, if an effect such as <Security A.> is given to a Digimon that isn't affected by effects, the Digimon won't be considered to have that effect.
Source: EX8-073 Gallantmon (X Antibody)