Yes and no. I think party politics do play a role in that a lot of candidates who are supported by the traditional party structure are perhaps more likely to be "traditional" candidates (more moderate, less diverse). As was discussed earlier though, and as you point out, women don't win at a lower rate than men once they're in the race they just don't run at the same rate.
Arguably this is more evidence of a system structured to preserve the status quo, which at the end of the day strikes me as discernibly more "conservative" ideology than "progressive."
There are a lot of studies and theories out there on minorities and women (who are not a minority) running for office and why they choose (or are chosen over) not to run. Most agree there's systemic bias, the real question is pinpointing what that bias actually is and how it is propagated most "effectively."