The MacArthur New Testament Commentary has this to say:
There is a word in the Old Testament for “slave” that appears eleven hundred times, but in your English Bible [KJV] it’s translated “slave” once.
If you go to the New Testament, you will find the Greek word for “slave” about 150 times in all its forms. And you will find it actually translated “slave” only a few of those 150 times. The New Testament translators only translate the Greek word for slave “slave” when it’s referring to an actual physical slave, or when it’s referring to an inanimate object, like “slaves of sin” or “slaves of righteousness.”
To look at a vey clear example, few would doubt that Onesimus was a slave. His name, Onesimus, meant 'Useful' which was a common name in Greek society for a slave born into bondage, and in the Epistle to Philemon Paul asks Philemon not to punish Onesimus harshly for running away, or for any damage he had done when he left. The KJV Bible refers to him by the euphemism 'servant', although some Bibles such as NAB use the more honest description of 'slave', as in Philemon 1:16:
KJV: Not now as a servant, but above a servant, a brother beloved, specially to me, but how much more unto thee, both in the flesh, and in the Lord?
NAB: no longer as a slave but more than a slave, a brother, beloved especially to me, but even more so to you, as a man 13 and in the Lord.
The reference to 'servant' in 1 Corinthians 7:21-22 is compared to being a freeman, and clearly a reference to slaves. Once again, we see the KJV use the euphemism 'servant', while the NAB says 'slave':
KJV: Art thou called being a servant? care not for it: but if thou mayest be made free, use it rather.
NAB: Were you a slave when you were called? Do not be concerned but, even if you can gain your freedom, make the most of it.
The MacArthur New Testament Commentary says there is this concept of slavery in the Scripture that has been completely hidden to the English reader [although a few recent Bibles have begun to use the term 'slave']. The word is doulos. In the Greek, that word means “slave”--never means anything but “slave.” It doesn’t mean “servant”; it doesn’t mean “worker”; it doesn’t mean “hired hand”; it doesn’t mean “helper.” There are six or seven Greek words that mean “servant” in some form.
The Commentary explains that Calvin and John Knox and other translators putting together the Geneva Bible made a decision not to translate doulos as 'slave' because there was too much stigma with the concept of being a slave. So they opted to cover the word by replacing it with 'servant' or 'bondservant', and eliminated the word 'slave', except when the New Testament talks about an actual, physical slave, or an inanimate object, like slaves of sin or righteousness.
'Politically correct' is a modern term but, yes, the translators were being politically correct in their choice of words.