For a number of years now, I have been asking for a name for a specific logical fallacy. The fallacy goes like this: If person <a> and person (or group) <b> agree on topic <x>, then they must agree on topic <y>. I first came across this when a libertarian told me that since Karl Marx supported a graduated income tax and Abraham Lincoln supported it as well, then Lincoln was a Marxist.

You appear to be saying that since Elagabalus agrees with the Episcopalians on a few specific things, he is therefore an Episcopalian in his heart.  You are using the fallacy that I stated in my first paragraph.