To avoid equivocation, we need to drill down into the forms of servitude as mentioned in the Bible.
One way to break down servitude is between voluntary servitude and involuntary servitude.
Voluntary servitude includes debt servitude (bondservant), where a person under debt can not pay the debt back, so they work for someone for a fixed number of years. I think we can all agree voluntary servitude is not immoral since people freely choose to be a servant.
Involuntary servitude could be considered immoral since it is servitude against their will. Involuntary servitude includes war slaves and kidnapping.
Another way to look at servitude is the relationship between parties. In this sense, it is not immoral.
Moses and David were said to be servants of God:
Num 12:7 KJV – My servant Moses [is] not so, who [is] faithful in all mine house.
2Sa 7:5 KJV – Go and tell my servant David, Thus saith the LORD, Shalt thou build me an house for me to dwell in?
Servants in a household work for the master of the household:
Gen 24:34 KJV – And he said, I [am] Abraham’s servant.
People subject themselves to leaders:
Gen 42:13 KJV – And they said, Thy servants [are] twelve brethren, the sons of one man in the land of Canaan; and, behold, the youngest [is] this day with our father, and one [is] not.
1Sa 17:32 KJV – And David said to Saul, Let no man’s heart fail because of him; thy servant will go and fight with this Philistine.
We are to be servants of Christ:
Gal 1:10 KJV – For do I now persuade men, or God? or do I seek to please men? for if I yet pleased men, I should not be the servant of Christ.
There might be other broad ways to look at servitude in the Bible, but I think this covers the vast majority of cases. So, the only cases from above that could be immoral would be kidnapping and war slaves. I’ll post separate posts to deal with these.