I have read that Cross-loadings of below .3 are often ignored! Can I have some reliable references to back this up please?
I have read exisiting work and authors tend to make this decision without supporting their decision!
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A factor loading of $0.30$ means that approximately $10$% of the variance in the indicator is explained by the factor (i.e., $0.30^2=0.09$). Loadings lower than this are often considered unreliable or unimportant. The extent to which model fit is affected by constraining such loadings to $0.00$ can be explored using confirmatory factor analysis (CFA). I wouldn't call this approach "ignoring" them but maybe you had a different approach in mind. If so, please clarify in the question.
Edit: In the comments below, I provide some possible citations. Since you seem to want a more empirical treatment of this issue, I recommend Peterson (2000).