Spidey was an Avenger years ago and kept his identity secret.
That was a very different time.
The issue isn't about letting people onto the team only if their identities being known being a hypocritical stance because of their stance during the Civil War either.
The issue is trust. And trust is especially significant because of the Civil War, nevermind the Skrull crisis. For all they know, Spidey is working undercover for Tony.
ALL the members of New Avengers either have known each other for years or have another member that has known them to vouch for them.
Spidey is the ONLY member whose identity is secret. He is the ONLY member who not a single one of the team can vouch for.
And then throw into the mix the Skrull crisis. It makes no logical sense - every member of the team would put Spidey at the top of the list as most likely to be a Skrull.
Remember when Strange did a spell that showed everyones true self?
That memory as far as the characters are concerned as no bearing on Spidey. That spell strange did momentarily created some trust in the team - but how can they trust Spidey if they can't even remember his identity nevermind not being able to remember his true self being revealed?
They. Would. Not. Trust. Spidey.
Give me one single reason why they should trust him.