There is little evidence upon which this list is based, even after
extensive searches, and many of those records seem to be inaccurate, or
later corrected.
To quote Snopes:
We searched contemporary reports for each of the listed incidents in
an attempt to uncover any mentions of political affiliations,
motivations, or voting records. Many of these items can be traced back
to poor reporting, articles that were later corrected, or fake news
items. And although we encountered this meme (or a similar list) on a
variety of web sites, none of these publications provided any
documentation to back up these claims.
Verifying this information through online state voting registrations
proved problematic as deceased individuals are removed from these
databases. We reached out to state historical societies for additional
documentation, but several of the states we contacted told us that
voter registration records weren’t archived. Even if they were,
however, one’s official party registration can often contradict one’s
political beliefs.
Given the difficulty of finding the political affiliation of many of
the individuals on this list, we are highly skeptical that this list
is based on credible information.
Source: this Snopes article which examines the claim in considerable detail.
The Snopes article goes through the 20 claims one-by-one. One can refer to Snopes for the details, but net-net is that Snopes rated one item "mostly true" (Lee Harvey Oswald), eight items "false" or "mostly false", and 11 items as "unproven". In general, the "unproven" decision was due to a lack of any hard evidence as to the political affiliation of the shooter.
I'll add the historical observation that, between roughly 1900 and 1964 the Republican and Democratic parties almost exactly switched sides philosophically. So claims that someone was a Democrat in the 1800s, (the Lincoln and Garfield assassinations), is essentially a claim that they would be a Republican by today's standards.
Relevant to this historical observation:
Is it true that Jim Crow laws were primarily promoted by the Democratic Party?
