If we hold to Bible references not being culturally dependent, then it is a sin for a man to have long hair, for women to cut their hair short, and being in church without a head covering. Also, it is a sin for a women to speak in church and to have any involvement in the Sunday service. And yet, the majority of churches have no problem with these things, and missionary organisations depend on women to do the bulk of missionary work. So if you going to apply strict transcultural principles to these matters, you would have to prohbit men having anything other than short, back and sides hair, women to have long, uncut hair, and every woman to wear a head covering in church, and sit in silence, not even to be able to teach Sunday School, and have no women on the mission field preaching and teaching the people. Also, you will have to condemn women who wear trousers and male style suits to work, and who have executive positions in the workforce.
It's more complicated, than biblical commands not being culturally dependent.
You need to more carefully define "culture".
Some cultures are compatible with Christianity, at least in some areas.
Some cultures are incompatible with Christianity, at least in some areas.
I would argue that God gave his people a divinely inspired culture, and THAT
is not to be set aside as if it were merely a worldly culture.
At its most undefined understanding, ANYTHING can be considered as part of a culture,
so those who feel free to set aside "cultural" commands, could set aside ANY
command in Scripture. This is unbiblical.
Some biblical commands (such as to dress modestly) may be quite differently UNDERSTOOD
by different worldly cultures. But some of those understandings, may not be godly.
Some biblical commands, such as to the Jews on men not wearing women's clothing,
and women not wearing men's clothing, deal more with male and female uniqueness in
clothing, and less on specifics of male and female clothing.
When Paul argues about hair length, his argument is based on a global precedent,
that is the angels covering their heads before God Almighty. This is not a
"cultural" argument. It is an argument about authority.
While most Christian groups accept the special authority of the Apostles,
some denominational theologies do not. This reduces the authority level
of the Scriptures, as taught by one of the Apostles.
These are some considerations, to keep in mind.