It all depends on the context. It all depends on what happen. Is it happening now? Did it happen in the past? Did it not happen in the past but you are thinking of what would have happen?
Conditional Present Real or Present Unreal Conditional (see info below)
That said and after readin the grammar below, your sentence:
If neither of us is wrong, then the discussion wouldn't have been necessary in the first place.
The grammar is not correct. You should either say:
If neither of us is wrong, then the discussion was not necessary in the first place.
If neither of us had been wrong, then the discussion was not necessary in the first place.
More grammar on conditionals
PRESENT REAL CONDITIONAL
[If / When ... Simple Present ..., ... Simple Present ...]
[... Simple Present ... if / when ... Simple Present ...]
The Present Real Conditional is used to talk about what you normally
do in real-life situations.
If I go to a friend's house for dinner, I usually take a bottle of
wine or some flowers.
When I have a day off from work, I often go to
If the weather is nice, she walks to work.
Jerry helps me
with my homework when he has time.
I read if there is nothing on TV.
IMPORTANT If / When
Both "if" and "when" are used in the Present Real Conditional.
"if" suggests that something happens less frequently. Using "when"
suggests that something happens regularly. link
The other option is:
PRESENT UNREAL CONDITIONAL
[If ... Simple Past ..., ... would + verb ...]
[... would + verb ... if ... Simple Past ...]
The Present Unreal Conditional is used to talk about what you would
generally do in imaginary situations.
If I owned a car, I would drive to work. But I don't own a car.
She would travel around the world if she had more money. But she doesn't
have much money.
I would read more if I didn't watch so much TV. Mary would move to Japan if she spoke Japanese.
EXCEPTION If I were ...
In the Present Unreal Conditional, the form "was" is not considered
grammatically correct. In written English or in testing situations,
you should always use "were." However, in everyday conversation, "was"
is often used.link