It’s not so much who he traveled with that’s the issue. It’s who he *ordained*—who he consecrated and set up as leaders of the Church. Jesus picked only men like Peter, and those men picked only men like Linus, Cletus, and Clement. Then those men picked only men. Then those men picked only men. And on and on to today.
Meanwhile nobody among all those men seemed to care about nationality. Peter was a Jew, but he ordained Clement who was a Roman. There were Greeks, Syrians, Egyptians, and later on Gauls and Ethiopians. If Thomas indeed made it to India as tradition states, he probably appointed an Indian. You’d think that if there were a problem with nationality, it would have come out somewhere along the line. But it didn’t. So it must not have been a problem.
It’s Jesus’s Church, not ours, and while He gives us liberty in a number of different areas, no one ever thought, for 2000 years, that anyone had any liberty to ordain women to the priesthood. And this was, mind you, smack in the midst of pagan cultures who had priestesses, so I don’t think the opportunity wasn’t there.
Have faith; the church has changed before and the ordination of women will be a change for the better.