Not so sure. Watergate brought down a GOP President, if Nixon was a Dem, may well have been different.
The double standard has been in place a long time. If Nixon was a Dem, there is not doubt the press would have been leading the cover-up and Woodward and Bernstein would have either been marching in lockstep or trying to get jobs pumping gas or flipping burgers.
The only reason they met any resistance is because the story was such a nothing story, and their editors didn't want to waste their time with a story nobody would care about. It was a nothing story, but the constant drip made people think they should care.