Far more often than not, these 'therapies' are one side of a coercion-related issue, and that raises (or should raise) alarm bells everywhere for anyone who truly puts patients and their wellbeing first.
There are really only two ways that a practice of 'homosexual conversion' can come into existence, either:
some people have a philosophical (religious, societal) view that other people ought to have their sexuality changed; or
some people of their own volition seek help to change their sexuality.
It can't really come from anywhere else.
But look at the implications:
Case #1: Attempts to "change" others:
In the absence of an objectively harmful personality trait - not just a prejudice or religious belief - case 1 implies changing others mainly because you/your religion/your sociopolitical system thinks they shouldn't exist as they are (or even don't have a right to exist as they arre), even if it does no harm. If that doesn't raise alarm bells, it should.
As a starting point, whether or not sexuality is hard coded or not ('nature vs nurture') we can agree it is a deep and fundamental part of personality/"who we are" for many/most people, so changing it will usually be painful, raise deep conflicts, and probably cause long term psychological impact. If the person themselves doesn't wish it, and their present state is harm-free, then there simply isn't likely to be a gain appropriate to the risk.
Changing others because "we know it is how they should be" or "we know they will be happier" is usually flawed the same way.
Of course we know more than this. We know most of these cases of 'conversion therapy' instead do harm (we have and see reports), and we know they are overwhelmingly fuelled by societies and religious views that deeply disapprove of what they wish to change. So they are not even clinical motivated people, seeking least harm; those making such referrals or offering such 'therapies' are motivated by their beliefs that it is right to change others, and they likely to have (and often do have) a view that any enduring harm is justified/acceptable provided the person can be changed/saved/returned to 'right thinking'.
There are few things more poisonous than being convinced "I known what is best for someone else" or "I know how all people should be", if you really only know what your own beliefs are about what is best for them.
If that isn't enough to say "no" and enforce it in law as a form of pseudoscience medical/clinical/professional abuse, it should be.
Case 2: Self referral to change oneself:
Case 2 is equally problematic. A person wishes to change. We could argue that a person is entitled to want to change. Well, yes. But we need to be very careful before assuming that what we see is the reality.
In some cases, that may be quite legitimate and the reality. But one may have a concern (perhaps without proof) that this is far more often often a result of coercive pressure, which the person feels distressed by. For example, ostracism, disapproval of peers, bullying, and in many places risk of physical violence or death. Coercion could be blatant, but it could be unconscious or 'locked away' (denial), may be related to abuse/fear/assault in childhood, or it may be an external view absorbed and accepted over time, perhaps from far back in early childhood.
These seem far more common motivations for self referral, and should make us cautious about assuming it's truly what a client truly would ask for, in the absence of such past/present/outside pressures. Even in non-sexual therapeutic work, self understanding is often quite mistaken at the start, and the aim is to aid the client to recognise what is happening in them. But coercion on sexuality is so prevalent in society, and starts from birth (boys are like this, girls are like that), that an ethical therapist will take some time to explore this first, or at the same time, and not just assume, if a client arrives and asks to 'be changed'.
We can find more evidence by critically examining the wider context. If these people (who self refer) were truly motivated by their inner feelings, and not by a sense of what they "ought" to be or concerns of external acceptance/rejection/fear/coercive pressure, we would expect also to see some minority, however small, of heterosexual people self referring for 'conversion therapy' to be homosexual as well - but we don't at all.
That should raise really big alarm bells - why would referrals be one way only, when we know homosexuality is widespread in nature and in humanity, and especially when we know there is immense pressure that way but not the opposite way?
Maybe because one way is somehow "natural"? I don't think so - people who self refer would probably not give as a reason, "I feel perfectly happy being gay and all is fine, and no religious belief or social pressure or fears affect my decision, but philosophically it isn't natural so I'd like to change my sexuality anyhow, please help me."
Mainstream professional approaches:
The usual solution in psychiatry/psychology is not to seek and coerce pre-determined change. Rather, it is to help the person to grow and overcome their distress, or to develop ways to handle it. For example, a person might need to learn that they can "be themselves", or develop inner strength to handle a conflict in their lives, or to look at where a fear or feeling comes from.
These are rather more helpful approaches than trying to 'change' people to fit preconceptions. If that self-discovery leads to a change in sexuality, so be it. But the difference is, it would stem from healing rather than expectation.
How can we know this? Because unlike 'conversion therapies', when people do self-refer for sexuality related conflicts and it's not a coercive approach, we DO see two-way traffic. We see married men/women who discover they are gay/bisexual, as well as gay people who discover they are straight/bisexual, as we might expect.
That said, help directed at a specific change may be valid in some cases:
There are also of course cases where it may be valid to help someone with their sexuality.
For example, in real world situations where a person is conflicted, or faced with desires that don't fit their preconceptions, they may become less pained if they can examine the nature of their attraction and feelings. But this isnt conversion - it doesn't set out to take a person who feels sexuality A and 'convert' them to feel sexuality B.
Also if a person's sexual choices are actually capable of harm, there would be a real motive for attempting to make a specific change of that kind. I'm going to skip this obvious case because (1) it's obvious, (2) it's off topic, and (3) the obvious example is paedophilia and enough ignorance has been said conflating that with homosexuality that, to me, it would feel offensive to go there.