I think it is good to be honest about apostasy in Islamic law and thought. There are roughly three views that are espoused about this:
(a) The ruling that an apostate should be killed (except in certain cases) is correct and in line with the Prophet's teachings.
(b) In the past, in and around the Islamic regions, religious identity was like today's national identity. So, in times of war, apostasy was equal to defecting to the enemy's side and was equivalent to treason. This is why there was a strict penalty for apostasy, just like, in today's world, a person who commits treason to their nation-state is often considered worthy of death. However, today, identity is primarily based on nationality not religion, so this no longer applies to the world.
(c) The ruling that an apostate should be killed is incorrect and based on inauthentic material, and this idea goes against the Qur'an which says there should be no compulsion in religion.
One can also add factor (d): That, due to the challenges the Muslim-majority world has faced due to the legacy of colonialism and a sense of being under threat (politically, economically, culturally, etc), there is an increased sensitivity against people who might be seen as threatening the faith.
So, those are some of the possibilities, and I think it's worthwhile just to discuss them as they are.
In practice, apostasy law tends not to be practiced. Also, most Muslims tend to be uncomfortable with the idea of punishing apostates. Of course, this is not to diminish anyone's experience who has dealt with this.
Some opponents to Islam argue that it is only due to this law that Muslims remain great in number, but that is obviously not true since the vast majority of Muslims do not base their faith or religious practice on this law. Rather, they choose to practice voluntarily. It is very difficult to force someone to be genuinely dedicated to a religion.
Furthermore, if it were only due to fear that Muslims were remaining Muslim, then why would Islam have inspired such a vast outpouring of religious culture such as Islamic literature, mystical poetry, theological writings, Islamic art and architecture, and so forth? Physical manifestations of a person's faith suggest that their faith is genuine.
It is also quite rare to find a Muslim who wants to leave Islam but who says they are staying in Islam because of this precept of Islamic law. Possibly there are some, but it is certainly not the norm.
While conversion away from Islam is not extremely frequent, the vast majority of people who are believing Muslims tend to stay Muslims for their own reasons, not out of fear of this ruling in Islamic law.
Perhaps these non-Muslims can simply talk to Muslims, ask them about their faith and why they hold it, and this will give them more insight into what actually happens among Muslims.
Might I suggest as tactfully as possible that Islam does not have a history of an Inquisition or forced conversion (for instance, during the slave trade in the Americas), or Crusades, the same way that Christianity does. Historically, Muslims have tended to acknowledge and respect religious diversity reasonably well.
I don't wish to reduce this to a debate about whether Islam or Christianity is better or paint Christianity only with that brush. I am just saying that it is important to recognize that Islam and Christianity have different histories and sometimes there may be an erroneous tendency to project what happened in the history of one religion onto the other. Also, if some of these non-Muslims are coming from a Christian background, they might benefit from being more self-reflective about their own history rather than pointing fingers at Islam.
In fact, it can be argued that negativity against organized religion in some of the West is due to forms of suppression due to the Church in the past few centuries. Some people who have had a bad experience with the Church then also project that negativity onto other religions, assuming that all organized religions are exactly the same, but this is a myopic viewpoint. So, if this is a factor in the discussion, I would again suggest that they actually talk to real, living Muslims (not sensationalist websites or ex-Muslims seeking attention in the media) to get a sense of what actually tends to happen in the Muslim religious experience.
However, I have noticed a curious phenomenon about apostasy and Islam: one never seems to wholly leave Islam. That is, anyone who leaves Islam and formally converts to another religion perpetually seems to identify themself, and be identified as, an "ex-Muslim". In contrast, a Buddhist who becomes a Christian is usually referred to as a "Christian", not an "ex-Buddhist". I suppose this says something about the world we live in, or perhaps Islam just has a strong staying power when it comes to identity.