Romeric is a duaric orientation, referring to MLW (men loving women). A julietian woman may or may not be attracted to other genders as well. It can refer to straight men, bisexual men, pansexual men, and any other men who experience attraction to women.
The term is typically not used as an orientation on it's own, though can be if desired. The term is commonly used by non-straight men to talk about their attraction to women (though straight people are included in the definition). It can also be be used as an identity for men who know they are attracted to women but are unsure if they're attracted to other genders, or by men who are attracted to multiple genders but want to emphasize their attraction to women.
The female equivalent to romeric is julietian.
History
The term appears to be coined along with the flag on June 27, 2018 with a submission to the Tumblr blog beyond-mogai-pride-flags[1]. The names romeric and julietian were based off Romeo and Juliet.