From this theory, did Cap really get married to another Peggy from another reality?

Since that reality's Cap, which at that point also probably frozen, will definitely also love that reality's Peggy, does this world's Cap really had any business there except to intrude into that dimension's Peggy and Cap relationship? What happens when that reality's Cap is woken up? Wouldn't he be also looking for Peggy as this reality's Cap also did?

While that reality's Peggy still looks, feels and acts the same, she would definitely still be a totally different person to this reality's Peggy.

Is what Cap is doing morally defensible?