As far as your questions:
I would trust some people who identify as Republican, but not others. I would trust some people who identify as Democrat, but not others. Out of the two sets, I would trust the ones whom I personally know, and not anyone else, no matter who they say they are.
In the following scenario, I would trust both a Democrat and a Republican fact-checking Trump's claims of election fraud;
[Me] #trust [My friend Alice, whom I trust to assign trust responsibly] #trust [Alices's friend Bob, whom Alice trusts] #trust [...] #trust [Democrat fact-checker] #approve fact-checking report.
Depending on the Bacon number and how many other similar connections there are, I would trust them more or less.
If there are no connections, then I wouldn't trust them beyond the distance I can propel their supposedly human body under my own power in Earth's gravity.