Is it permitted for a man to apply makeup to a woman for the above reason?

If that’s his profession, then yes.

Could the Rabbi please sharpen the answer? Seemingly, the whole craft of the hairdresser / makeup artist is to beautify the woman, so in practice he is occupied with her beauty. How does the permission of being preoccupied with his professional work help here?

That has nothing to do with it. If it’s his profession, then her beauty is, in his eyes, a technical matter.

1. So why are there rabbis who forbid it? They say a woman can easily go to a woman.
2. How far does this boundary of being preoccupied with one’s work go? Is it permitted to go to a female massage therapist if the client is a man (Swedish massage, Thai massage, etc. for muscle relaxation)?

You should ask them. In any case where this is a person’s profession, this permission is relevant.

1. When it says “site staff,” who is answering? Only Michael Abraham, or are there other Torah scholars here answering as well?
2. I’d be very grateful for more explanation of how this permission is relevant in every profession. My friend studied treatments like Swedish massage and aromatherapy, and afterward she became religious. She also wanted to continue studying additional massage methods and looked for work, but almost every spa or hotel required her to work with men too, so she couldn’t find a job. She also couldn’t find non-mixed study programs (maybe they exist, but far away and difficult). In any case, all the rabbis she asked told her that it isn’t modest and that it violates the prohibition of touch, because this is only massage for general health and not some serious medical treatment like physiotherapy. And why should she do something not kosher if she can make the effort to find only female clients? (But she wasn’t able to start a business on her own.) So does the Rabbi hold that there is no issue of modesty here? No issue of touch?
Does the Rabbi not hold that a person should make a great effort to work only with members of his or her own sex? The rabbis basically told her: then give it up—if you can’t manage, work in something else. That’s devotion to God’s word, just like you wouldn’t work at this on the Sabbath, so too don’t work with men. So what does the Rabbi think about that?
Thank you very much.

The headings are not relevant. The answers here are only mine.

This permission is relevant in every profession when the concern is forbidden erotic thoughts. “Preoccupied with his work” means there is no concern for such thoughts. When we are dealing with an occupation that involves an actual prohibition beyond forbidden thoughts—and there are disputes about this in various contexts, such as touch and seclusion. But in my opinion, quite simply, both of those too are because of erotic thoughts—some have written that in such a case the permission of being preoccupied with one’s work was not said. Although I seem to recall that there are halakhic decisors from whom it appears that even in such cases they permitted it.
Many halakhic decisors wrote this regarding a gynecologist and physiotherapy, and I do not see a difference between that and massage and the like. This is not a permission because of need (for then there would be room to distinguish in a place where there is no acute medical need), but a permission according to the law itself.
All this is said according to the halakha and the strict letter of the law. Whoever wants to be stringent beyond the letter of the law, blessings upon him, but that is left to each individual and his own considerations.

One should also add here considerations of “it is unavoidable and not intended, where there is no other way,” but this is not the place to elaborate.

Honorable Rabbi,
Thank you very much for the answer (of course I’d be happy if you could expand a bit more or direct me where to read about what you said regarding the disputes over whether this is also because of touch—it isn’t a problem that the women are menstruants?—and seclusion, or only because of erotic thoughts).
Thank you.

As I recall, Rabbi Heber has a book on modesty, and he discusses all this there at length.

Are massages done in full nudity also okay according to this reasoning?

In principle yes, as long as that really is how it is done for the professional purpose. However, there is also an issue of modesty as an independent value, and according to that there is a problem here beyond forbidden erotic thoughts, and perhaps it would be forbidden for the patient (though not necessarily for the therapist).

Thank you for the answer.
1. Regarding the book, I’d appreciate it if anyone knows the name of the book please—and what is Rabbi Heber’s full name?
2. Actually I also wanted to ask about the side of the patient: if it could be forbidden for him, then does the therapist bear no responsibility on her side? Like “do not place a stumbling block” or some other prohibition?
Thank you very much, and Sabbath peace.

https://tablet.otzar.org/book/book.php?book=163599
I don’t think so, since if she doesn’t do it, someone else will. At most it would be merely assisting, and even that is very doubtful.

Have a good week, and thank you very much for the response. I’ll read it.

In the book A Time for Modesty Is Wisdom I didn’t find any discussion of this issue. I’d appreciate it if the Rabbi could point me more precisely in the right direction.
Thank you very much.