There is an issue of cross-loadings in my output results after running an EFA with varimax rotation. Should I ignore these cross-loadings since these differ by more than .20?
The above results look like you might have various measures and therefore questions that are supposed to load on various latent factors and not others, and if that is the case a Confirmatory Factor Analysis may be warranted. But you may also try a more flexible approach, see:
Marsh, H. W., Morin, A. J., Parker, P. D., & Kaur, G. (2014). Exploratory structural equation modeling: An integration of the best features of exploratory and confirmatory factor analysis. Annual review of clinical psychology, 10, 85-110.
I'd try oblimin rotation assuming factors aren't orthogonal. One of Polish masters in psychometrics (Hornowska, 2011) suggests ignore factor loadings only if they are under 0,30. As I see, some of Your "lower" cross-loadings are about 0,40.
Thank You Karol Karasiewicz Jeffrey Martin for your valuable inputs. I tried oblimin rotation with PAF which is coming out neat with lower cross loadings, however component correlation matrix suggests low correlation in between one of the items as given in the picture