Do Anglicans feel uneasy about the fact that their tent is so large and that it could simply be meaningless?
I'd dispute that it is or could be meaningless. On the contrary, I think it is a strength.
I do get grumpy sometimes because I think we have some clear boundaries, and there are people who cheerfully ignore those boundaries, and it's the lack of integrity, as much as anything, that I then struggle to respect.
I wrote this some years ago, as a very personal reflection on this, and it might give you some insight into my take on it:
Why I love my diocese
And also - speaking out of my background having studied population genetics - diversity is incredibly important in a population under challenge. If you have a population (for the moment, let's think of that as a collection of parishes) which are all very alike, then if a time of difficulty comes to which that particular, narrow tradition doesn't respond well, your community of faith can easily become extinct. But if you have a population which has great diversity, then when times of difficulty come, it is more likely that, in that diversity, one or more of the strands of that tradition will be able to adapt and respond well and continue to grow and thrive, carrying the life and mission of the church forward.
In God-given and hallowed diversity lie the seeds of the continuing mission of the church, as societies and cultures change. Wisdom is vindicated by all her children, and we would be wise to honour that.