“May we respect and love one another as brothers and sisters”
Unless you are a swami mind reader, there is no specific equating of, “as brothers and sisters”, to mean “you are our Christian brothers and sisters”.
It is a simple call to love one another. Any other assumptions are simply that, and appear to stretches, with no foundation.
I'm going by "context" -- pretty simple really. Unless you are a swami mind reader and can prove otherwise, I'm pretty comfortable connecting the dots that seem to me to be pretty obvious.
Another poster mentioned earlier upthread that if he meant "brothers and sisters" in the sense of we are all humans.... I can buy that. However, I haven't seen those terms used outside of a faith-based connotation.
Hoss