Is the Frankenstein franchise antisemitic?

First of all, the movie is of course based on Mary Shelley's 200 year old book, so your theory either applies to the whole franchise, as started by the book, or to the 1931 movie alone (which wasn't even the first movie), and I have never heard about any signs of anti-semitism analysed into Mary Shelley's work (though this may be just me and someone has already picked up that theory before). So we could actually devitalize the first two of your points, since they come directly from the book, but I've still listed them here, as they're the most easy to devitalize by common sense:

The name "Frankenstein" is a very Jewish name.

Even more than that it is a common German name and as we all know from the 200 year old book, Frankenstein was "by birth a Genevese". And also his family was "one of the most distinguished of that republic" which I would dare to say wouldn't hold so much for a Jewish family 200 years ago.

The creator is Dr - a common Jewish profession.

Huh? Well, it may be regional (or rather historic) reasons or ignorance (since I and most of the people I know don't really care about religion), but I know a thousand doctors (exaggeration intended) which are not Jews. And I also have never heard of such a cliche. Had he been a banker... (don't take that seriously, I don't want to support that cliche either).

And from your usage of the word "creator", I hope you don't mean the creator of Frankenstein, because that was Dr Victor Frankenstein's father (well, in fact his father was a doctor, too). You of course know that the creation is not called Frankenstein.

The townsfolk (symbolised by pitchfork {ei. farmers - not a common
Jewish profession}) attack the "Jew" and burn down his house (the
historic practice of "firing" was a common way to get someone out of
your town).

Well ok, I don't remember that happening in the book. It is true that for historical reasons going back to medieval times Jews were indeed only allowed to a limited range of professions, none of that being farmers, I think. But still farmer is a very common human profession and I would rather see it as a symbol for the rather simple minded of people than for good Christians. And in fact driving someone out of your town by violence and burning down the house was probably not only done to Jews, I guess.

The movie came about in the 1930s when anti-semitism was just about to
peak.

Ok, I don't know much about the situation in the US at that time so I cannot say this is true, neither do I know about The director's/writer's background. But in Europe anti-semitism IMHO didn't get "really popular" until two years after the movie. Other than that anti-semitism has always been "popular", even if not as drastic as in the last century.

Is there any history or solid evidence that Frankenstein is
anti-semitic,

I don't think so, but maybe you find some remote analyst having tryed that weird theory before.

or am I just reading into it too much?

Most probably. Maybe the fact that in the US somebody called ...stein often is Jewish (as iandotkelly explains in his comment) might have confused you.

As as side note, if you want to see a movie that is IMHO both in its story, but even more so in its tone and moral, much nearer to the book (though not perfectly either), I recommend Kenneth Branagh's 1994 version. Or rather just read the book, which is really good, too.