Omniromantic

Omniromantic is an orientation defined as the romantic attraction to all genders, though gender often still plays a role in one's attraction. Some individuals who identify as omniromantic may have a preference to which gender they feel most attracted to. For others they may be equally attracted to all genders, but they may feel the act of being attracted to one gender feels different than the act of being attracted to another gender. They might also find certain traits only attractive in certain genders.

The sexual counterpart is omnisexual.

Omniromantic vs. Panromantic
Panromantic and omniromantic are very similar as they both involve the attraction to all genders, however one can make a distinction between them if they wish (for example: an omniromantic individual may feel like the act of being attracted to a non-binary man feels different then being attracted to a non-binary woman). For panromantic individuals, they often do not feel any internal difference between genders.

Omniromantic individuals are also attracted to all genders, much like panromantics, but omniromantics tend to feel a difference between genders. This can manifest itself as a preference for certain gender(s) (though omnisexuals do not need to have a preference). Omnisexual individuals may also feel as those the act of being attracted to certain gender(s) feels different from being attracted to other gender(s). They might also find certain traits only attractive on certain genders.

Etymology
The prefix omni- comes from the Latin word omnis, meaning 'all'. Pan-, which the term panromantic comes from, also means ’all’, and is a Greek prefix.