I'm writing a story in which a character's birthday (May 1st) is significant. A characters notes in conversation that, "Her birthday is May first." Should I write out 'first' or refer to it as '1st'? If I write out 'first', is it capitalized or not?
I would personally prefer to see 1st.
I cannot imagine first should be capitalised but I would have to read it twice to understand May first or May First — since May can be a name of a person and first can mean before something else.
How about "on the first of May" or "on the 1st of May"?
Here is the nGram for first of May,1st of May,May First,May first,May 1st
Particular dates use numerals. They are particular objects, referring to particular points in time, just as names refer to particular people.
If it was instead a relative date, such as seven days from now, then we would spell it out.
If it was a relative day of the week, it would appear as text, such as the sixth day of the week on my calendar is Saturday.
As it is on a particular date, like May 1st, use the numerals or digits.
For more guidance on numeral or digit usage, you may want to look at the different style guides, such as the MLA or APA: