Among LGBTIQA continuum, most Bible-based groups have the most positive attitude to asexuality, thought it does not happen always. Many of these groups have that all the people should get married and have some discrimination toward single members. However, in fact, in the Bible, the attitude to asexuality is very positive. Read 1 Corinthians, ch. 7 and 9:5, for example. Even apostle Paul was single.
Intersex people experience more discrimination in Bible-based groups. For example, some groups consider that these people are under God's curse. However, the fact is that the Bible never mentions intersex people. Likewise, it does not mention people of many races and nationalities. Does it mean that they are under God's curse? Of course, not. Some groups even say that intersex people were not created by God. However, in Genesis 1:27, it is said (NIV):
So God created man in his own image,
in the image of God he created him;
male and female he created them.
This verse does not teach the binary of men and women. It does not say that God created some people men and some people women, although it is how it is commonly understood. In fact, this verse even may imply that all human beings have some male and some female traits which is scientifically correct. For example, both men and women produce testosterone (male sex hormone) and estrogen (female sex hormone), but in different proportions. So, this verse vindicates intersex people rather than condemns them.
Most Bible-based groups teach that transgender people, including transsexuals, live in serious sin. They are often excommunicated. Although most Christians believe that transgender people sin, the Bible practically does not mention them. The only verse that can be applied to both MTF and FTM transsexuals is Deuteronomy 22:5 (NIV):
A woman must not wear men's clothing, nor a man wear women's clothing, for the LORD your God detests anyone who does this.
It is quite interesting that most Christians completely neglect the whole chapter 22 of Deuteronomy, but believe that v. 5 should be practiced. Interesting, why do they think this way? Deuteronomy was written for Israelites and is a part of Jewish law. There are many different hypotheses why this commandment was prescribed to Israelites. It may be that cross-dressing was a part of pagan rituals or that men or women cross-dressed in order to get some privileges or avoid some duties. There are no indications that this verse should be observed now or applied to transsexuals or cross-dressers.
There are also attempts to apply some other Old Testament verses to MTF transsexuals, for example, Deuteronomy 23:1 (NASB):
No one who is emasculated or has his male organ cut off shall enter the assembly of the LORD.
Then, what about men who lost their genitalia because of an accident? This verse does not say anything about the reasons why genitalia were cut off. This verse was written for Old Testament Israelites, not for Christians.
Regarding gays and lesbians, again, most Christians are sure that their behavior is sinful. Apparently, the Bible does condemn homosexuality. However, in fact, it is a matter of traditional interpretation of the Bible rather than what the Bible really says. It is quite remarkable that sometimes Christians had to change their interpretations of the Bible when they contradicted science. For example, in the past, Christians believed that the Bible teaches that the sun goes around the earth and resisted Galileo's and Copernicus'. Later, Christians admitted that they were correct and had to change their interpretation of the Bible. Christians also used to believe that the universe was created in literal 6 days and it happened 6,000 years ago. Most modern Christians do not believe it because it contradict science. There were invented many interpretations of Genesis, ch. 1.
Most Christians believe that Sodom was destroyed because of the inhabitants' homosexuality and draw this conclusion from their attempt to rape Lot's guests. However, raping is obviously evil whether it is homosexual or heterosexual. The Bible does not say that Sodomites' sin was homosexuality.
There are some other Old Testament verses that are used against gays and lesbians, for example, Leviticus 18:22 and 20:13 (NIV):
You shall not lie with a male as one lies with a female; it is an abomination. (18:22)
If there is a man who lies with a male as those who lie with a woman, both of them have committed a detestable act; they shall surely be put to death. Their bloodguiltiness is upon them. (20:13)
However, how many Christians believe that all the other verses in these chapters should be observes, such as 18:19 that prohibits sexual contacts during periods or 20:9 and 10 which say that people who curse their parents or commit adultery should be put to death? Again, these commandments were given to Israelites, not to Christians.
Romans 1:26-27 are also often used in order to condemn homosexuality:
26 For this reason God gave them over to degrading passions; for their women exchanged the natural function for that which is unnatural,
27 and in the same way also the men abandoned the natural function of the woman and burned in their desire toward one another, men with men committing indecent acts and receiving in their own persons the due penalty of their error. (NIV)
However, the problem with these verses is that for gays and lesbians homosexuality is natural and heterosexuality is unnatural.
Thus, the Bible does not condemn LGBTIQA people, even though Christians do.