Franklin didn't have the tools and process for determining the structure of DNA, only Watson and Crick did, because they used actual physical models to measure the angles and positions of the molecular components.

Further, by the time Watson and Crick did their work, Franklin had already left to work on the tobacco mosaic virus (TMV)[0].

That Watson and Crick could only nail the structure of DNA because of her crystallography work is almost certain. That she would have discovered the structure of DNA without them and their process/approach is a furphy[1]. It's their combined efforts which made it possible, with Franklin's work being the pointer in the right direction and confirmation, but Watson and Crick's being the bulk of the heavy-lifting necessary to map the molecule structure.

In the end, she probably didn't share in the Nobel because she died before the prize was awarded for the research.

[0] https://www.cinz.nz/posts/rosalind-elsie-franklin-1920-1958 [1] https://en.wikipedia.org/wiki/Furphy

Photo 51 was Gosling's work, which Franklin had looked at briefly in May 1952 and had been ignoring ever since. She never worked on it. Gosling writes: "Rosalind was going to leave, so she suggested that I go down the corridor and give this beautiful structure B pattern, this photo 51, to Maurice." [Wilkins] This was in the context of Gosling returning to Wilkins, who was his original DNA-structure supervisor before Franklin began working with DNA.

Our era is no different.

But to take you at face value: Are you sexist and racist because of politics, or is it simply because you're a bigot?

If it's politics, then just which political party do you subscribe to that has sexism and racism and bigotry as its guiding principles, hmmm?