When I was in the proofing process of my book, The Yellow Star That Wasn’t: Scandinavia, Miami, and Me: Wartime Jews in Scandinavia http://chofstadter.com/yellow-star-that-wasnt/ some proofers asked me about the spelling of antisemitism. Some insisted on capping the “a” in anti, while others were absolutely certain the term required a hyphen and/or a capital S.
I had struggled with this in all my writings (not to mention with the automatic spell-check that wanted its own way) till I found support for my own reasoning that, unlike the Holocaust, the concept of antisemitism does not warrant a capital letter.
The following plaque at the Jewish Museum of Florida, https://jmof.fiu.edu/ (located on South Miami Beach), now owned and managed by FIU, Florida International University, seems to settle the matter in a scholarly manner.
I, for one, am now a stickler for using “antisemitism” with the lowercase “a” and no hyphen (the beginning of a sentence gets the capped A, of course). But you may have to add this spelling to your on-line dictionary, which doesn’t automatically recognize it.
If you need a Holocaust scholar to back you up, just turn to Deborah Lipstadt’s outstanding book, Antisemitism: A Conversation for her section on Spelling.