Wilkins, along with Watson and Crick and many other men of that time, were misoginistic. A smart woman was a threat. Rosalind was smarter therefore men had to steal her work to try to beat her at the final discoveries.
To diffuse any situation, Rosalind would need to acquiesce to the men's needs. She was outnumbered. She was not outranked, but even superiors did not want to cause friction. They took the path of least resistance.
Wilkins could have worked in cooperation with Rosalind, but that way he would not achieve his selfish, manly goal.