This is a genuinely interesting theological and historical question. Here's a balanced look at the evidence:
Slave Ownership
The New Testament never directly commands Christians to free their slaves. Paul's letter to Philemon is the closest we get — he appeals to Philemon to receive back his runaway slave Onesimus "no longer as a slave, but better than a slave, as a dear brother" (Philemon 1:16). But notably, Paul stops short of commanding manumission. He leaves it to Philemon's conscience.
In Ephesians 6:9 and Colossians 4:1, Paul instructs slave owners who are clearly part of the Christian community to treat their slaves fairly and justly — which strongly implies that slave-owning Christians existed and were not automatically excluded from fellowship. You don't instruct people in how to do something you consider inherently sinful.
Polygamy
As discussed, the 1 Timothy 3:2 and Titus 1:6 argument is compelling here. The specific restriction on elders having only one wife strongly implies the broader membership wasn't held to the same standard — at least not initially or universally.
Jewish converts would have come from a tradition where polygamy, while declining by the first century, was never formally prohibited in the Torah. Gentile converts from certain regions had similar cultural backgrounds.
The Overall Picture
The honest answer appears to be yes — it was likely possible in the first century to be a Christian while owning slaves or having more than one wife, particularly if you were already in those situations at the time of conversion. The New Testament evidence suggests the early church worked within existing social structures while planting seeds of a higher ethic — what scholars sometimes call the "trajectory hermeneutic." The direction of travel was clearly toward equality, freedom, and monogamy, even if the destination hadn't been fully arrived at yet.
This actually strengthens the argument for progressive revelation — God meeting people where they are and leading them forward over time.