There can be no supposition of homophobia from an organization like the Audubon Society.
None whatsoever, by the organization or any of its staff? Do you have anything to back this assumption up?
And do you expect a person to research the history of every organization they interact with, or do you think it's useful for an organization to have something to quickly communicate to customers at a minimum "you're welcome here. You won't be hassled for being gay."
If we are to suppose homophobia everywhere, why not make it mandatory for everybody to display this?
Not everywhere, but it's certainly common.
I have no idea where your suggestion of mandatory Pride flags is coming from.
Would you imply that the non-display of a pride flag suggests that the individual or organization in question is homophobic? That would be ludicrous, in my view.
I think in the current climate, a business that makes a point of not acknowledging Pride Month raises the question of why they chose not to do it.
It isn't a guarantee of homophobia, but it at least suggests there's a non-negligible risk of it.
Why are we to suppose that any particular organization which has no apparent history of speaking out against homosexuality might be homophobic?
Because homophobia is pretty common in the US.
And in any case, there are other reasons for flying the Pride flag. When done sincerely, it can be about for remembrance and acknowledgement of the struggles that LGBTQ people have gone through and continue to go through.
It's kind of like wearing a poppy for Remembrance Day. It's still meaningful even without having to stand out against a background of people who are happy about soldiers dying in war.