Not to the early Christians it wasn’t. The early Christians movements (before they were co-opted by Empire) were radically egalitarian.
That would be irrelevant even if it was true. We are not in the second century. It is a very controversial position either way.
Egalitarian values certainly did emerge out of Christianity, and there was a change in that direction even then, but they were not egalitarian in the modern sense.
Also, please be careful when generalising early Christianty, as it was a very diverse group of sects that hardly agreed on anything.
Early religious communities sometimes were very accepting, and women played a role as well, but they still existed in a very patriarchal culture, so you should not expect their women to be equal to men in society, and there were absolutely positions of authority.
They opposed the empire because initially, they were not perceived by anyone as a group distinct from Jews, which were very hostile to it. However, there were appeals made by powerful Christians later to be recognized as a non-threat to imperial power, and ultimately, they succeeded.
Even so, the Jews simply wanted independence, not equality. The idea of social equality did not even exist then. They were equal in Christ, not in society.
Christianity was not coopted by the empire, it conquered it.
The idea that early christianity was somehow “more pure” I do not accept as well. I would say the Christian tradition has only been enriched over the years, and without a unified basic set of dogmas it would really make much sense.
If you are a country with a GDP that is 1000 or 10000 times higher it will not be a problem.