Mainstream Protestantism does not reject Catholicism nor Orthodoxy. There are some outlier Baptist and charismatics who seemed to have picked up issues, but even the SBC actively participates in ecumenical organizations with Catholics ad fellow Christians. I myself have been both Methodist and Orthodox and moved between the two with nary a look nor did I burst into flames. In fact the Orthodox Church took my Methodist Baptism for membership.
I agree, I think most major protestant denominations have no problem accepting Catholic and Orthodox Christians are legitimate Christians. The "Catholics ain't Christian" stuff seems to a fringe movement limited to some fundamentalist "born again" types. They'd also probably say most of their fellow protestants, and indeed, about 90% of practicing Christians in the world, "ain't Christian", since they only believe their brand of Christianity to be legit. History certainly isn't in their favor, the apostles themselves would be "non Christians" in their eyes.
>> I myself have been both Methodist and Orthodox and moved between the two with nary a look nor did I burst into flames. In fact the Orthodox Church took my Methodist Baptism for membership. <<
True, I think the rule of thumb for Catholic and Orthodox Churches is that a protestant baptism is valid as long as it's a tridentine baptism done with a traditional understanding of the Father, Son, and Holy Spirit. The vast majority of protestant churches fit that definition. Those that are non-tridentine often don't do the sacrament of baptism anyway. And non-Chrisitan churches like Mormons say "Father, Son, and Holy Spirt", but believe them to be three separate gods who "work together". Thus their baptism deviates from historic Christianity and what was established in the Bible, so it's not a Christian baptism. This isn't to say they're bad people though. Many Mormons behave in a more Christian manner than a lot of "Christians" in the world.