It doesn’t really map to either “fundamentalist” or “orthodox” in the usual theological senses (though its more associated with the former), particularly the “anyone capable of having children should strive to have more children” part, which is a modern social movement overlapping with some streams of Christianity, but not really a part of traditional doctrine.
> The only exception to all of this is choosing to become a monk or priest (depending on denomination) - in which case you owe a duty of faith to God and thus shouldn’t love other men or women anyway.
The branches of Christianity that have celibate religious brothers and/or clerical celibacy are also the most accepting of the concept of a vocation of committed single Christian life outside of clerical life and religious orders; there is basically no Christian community I am aware of where monastic/priestly celibacy is a norm but it is the only acceptable non-married life.
Also, different christian denominations have different beliefs about the purpose of marriage. Sex outside of marriage is definitely sinful in all of the mainstream christian churches, though they differ on how sinful sex is in the context of a marriage.
I'd also note that, while wedding ceremonies commonly talk of kids, there is no obligation to have kids as part of a marriage. For example, the church is perfectly happy to marry an old woman with a man, even though it is absolutely certain she can't have kids anymore.
Overall, the orthodox/fundamentalist christian position seems to be: sex should only be done for the purpose of making children, only married couples should have sex, and anyone capable of having children should strive to have more children. LGBTQ+ people are not exempted - at least if they are physically capable of having children, they shouldn't let their personal preferences get in the way of their duty to God - so they should also seek to enter a heterosexual marriage to have children. The only exception to all of this is choosing to become a monk or priest (depending on denomination) - in which case you owe a duty of faith to God and thus shouldn't love other men or women anyway.