To eradicate the views of heteronormativity, we need to work at deeper levels; the work needs to be done everywhere, even changing the language that portrays the existence of gender conformities.

It is not always appropriate to use "bride" or "groom" as everyone would not feel safe, respected or included in society.

Like using "Nearlywed" instead of saying bride or groom, the term implies that someone is engaged irrespective of their gender identity. Well, it is also appropriate to say engaged, but the word would intensify the meaning of the special wedding day.

Another one would look like a well-acquainted term as we often use it without knowing it's a gender-neutral term.
The word is "Fiance". It doesn't imply any identity when used normally unless the person using it specifies it by saying the gender. Therefore, this term is perfectly suitable for use.

"Newlywed" is also very commonly used, and it's a gender-neutral term; the only difference between Nearlywed and newlywed is that instead of being used before the wedding, it is used after. So instead of specifically mentioning husband or wife, you can just call them newlyweds.

Before introducing another one, we must understand that most of the terms already exist, but they need to be used more to make language gender neutral.

This one is "spouse". This is also used often instead of saying husbands or wives, and it could be made more accessible by just saying spouses.

We can also use partners, couples, or significant other for addressing people with different identities without specifying who they are.

There are many others to use for constructing a gender-neutral language that doesn't harm or disrespect anyone's identity. You can begin including it in your vocabulary while you speak; it will bring a difference.