There are two reasons for being very careful about the terminology we use.
We are not simply talking about actions. We are talking about people and those people can be hurt or offended by our words. This is made doubly difficult by the fact that what is acceptable seems to change regularly. It is not my desire to offend. All people are made in the image of God and are therefore worthy of respect. All people are loved by God and Christians are called to be like God in loving all people (Matthew 5:44-46).
The language is imprecise. There are people who are same-sex attracted (SSA):
but are celibate.
The reasons could include:
an understanding that acting on that attraction would be wrong
still seeking to understand that orientation and not rushing into anything
see nothing wrong with it but (at least for the moment) lack of confidence or opportunity or are simply choosing to be celibate
but, for whatever reason, are uncomfortable with that and struggle with it. Some may fail and feel terrible. Others may not fail but continue to experience the temptation.
and see nothing wrong with that, and are in a single, long-term relationship.
and see nothing wrong with that and have multiple relationships
and are actively engaged in a homosexual lifestyle and actively promote that lifestyle
who are in an exclusive heterosexual relationship
No doubt there are numerous other permutations as well.
The most general and least offensive term would seem to be "same-sex attracted" (SSA). That describes the sexual orientation but does not differentiate between those who are sexually active and those who are celibate. That is a distinction we will have to make.
But, there are related issues such as transvestitism, transsexualism, gender dysphoria etc. that are not specifically addressed on this site. LGBTQI seems to be an acceptable term but includes those additional sexual preferences.
This might change over time as the terminology changes or I become aware of the sensitivities involved but, in the meantime, I will use the following terms with the following meanings:
same-sex attracted person - to describe the orientation i.e. anyone who is attracted to a person of the same sex whether or not he/she acts on that.
homosexual - to describe the person who does engage in same-sex sexual activity (including those who are bisexual) that is, those who are sometimes called "practising homosexuals". "Homosexual" is the general term. Where it is important to specify female homosexuality, the term lesbian will be used.
N.B. I realise this could be confusing. "Homosexual" could be used in the same general sense as "same-sex attracted" but, on this site, it will be assumed that, unless otherwise stated, the homosexual person is sexually active.
celibate will be used when it is important to be clear that a same-sex attracted person is choosing to not be sexually active.
In this booklet, the two “sides” of the debate will be referred to as “conservative” and “liberal”. Those terms are not meant to suggest anything about the people involved other than to describe the two positions.
“Conservative” is intended to describe those who take a traditional approach that says that, from a biblical point of view, homosexual acts are sinful. They would argue that they represent the position the church has held for millennia and until very recently.
“Progressive” describes those who advocate for the rights of homosexuals to express their sexuality without condemnation.
You might prefer different terms. They simply need to differentiate between those who believe homosexual acts are sinful and those who believe they are not.