Can a married man have sex with a prostitute without breaking the third precept?

Can a married man have sex with a prostitute without breaking the third precept?

I think the Third Precept is put in place to avoid that exact situation of infidelity.

Take note of what it will do to the man who sees the prostitute (in the order of immediateness):

1. Financial Loss.
2. Loss of chances to treat his family right.
3. Risk of contracting diseases.
4. Increasing of thanha in the mind.
5. Risk of becoming a habit. Things we habitually do creates karma that are categorized as Achinna Karma. These are taken from one lifetime to another. So, there is a risk of repeating the same behavior. Achinna karma if remembered on the death bed will become Asanna Karma which in turn result being born in debasing places.
6. Definite action that will make the samsara longer.

If one can't live according to the five basic guidelines given by Lord Budhdha, can you call him/her a Buddhist?

In the Pali canon, sensual (or sexual) misconduct as one of the five precepts is defined as:

He misconducts himself in sensual pleasures; he has intercourse with women who are protected by their mother, father, mother and father, brother, sister, or relatives, who have a husband, who are protected by law, and even with those who are garlanded in token of betrothal.
MN 41

So for lay persons, it is more about adultery, infidelity, and a sensual relationship outside of a committed exclusive relationship (or marriage) with a free consenting adult (of legal age), rather than a specific sexual practice or fetish.

So, what's bad about sexual misconduct? What is the consequence that is to be avoided?

The minimum result it (sexual misconduct) leads to for a human being is rivalry and enmity.
AN 8.40

And what is the purpose of virtue?

"Skillful virtues have freedom from remorse as their purpose, Ananda, and freedom from remorse as their reward."
AN 11.1

Remorse typically comes from harming others in a way that you would not like to be done to you (Ud 5.1).

So, based on this, I would say using the services of a prostitute, without the consent of one's spouse or long term committed partner, violates this precept, as it may cause animosity with one's spouse and the betrayal of their trust, and result in remorse for the one who sought the services of the prostitutes.

Basically, if you would feel violated when your spouse or long term partner would use the services of a sex worker without your consent, then you should not do the same to your partner.

While I cannot site chapter and verse of the Suttas, but in my heart, for me the answer to this question is a strong no. There is no true way to know if any prostitute is having sex under duress. Also regardless of “allowing”by wives in certain countries the possibility of real harm is there. STDs, pregnancy, emotional harm to any and all involved.

DN 33 Commentary of 10 Akusalakammapathadasaka:

There are 2 kinds of 20 types of women, 8 by birth and 12 by agreement.

Breaking 3rd precept is for every man who having sex with 8 born-to-be-womens.

Breaking 3rd precept is for out-agreement-man who having sex with 12 in-agreement-women.

So, according to the question:

Can a married man have sex with a prostitute without breaking the third precept?

Yes, if his wife agrees with him to have sex with a prostitute.

The explanation I have heard regarding the third precept is for men to avoid having sex with certain types (20 types) of women. So my understanding is that a married man going to a prostitute doesn't break the third precept. Please explain if this is correct or not.

And that's the problem isn't it, the problem with seeing prostitutes is that there's no way for you, the client to verify with 100% certainty that the girl he's seeing does not fall into one of those 20 prohibited types! Quite often is the case that the girl is either under-age, or barely met the age requirement, already betrothed, married, or being victim of sex-trafficking industry and had to provide the service against her will, etc. So whenever there's uncertainty, it'd be better to err on the safe side by finding a legit. partner to engage in a legit relationship.

Wikipedia's Prostitution in Thailand says,

Buddhism in Thailand is largely of the Theravada school, which is followed by 95 percent of the population. "While Buddhism regards the celibate monastic life as the higher ideal, it also recognizes the importance of marriage as a social institution." Thai Buddhism encourages adherence to the fundamental code of Buddhist ethics for the laity. The Five Precepts contains an admonishment against sexual misconduct, although what constitutes misconduct from the perspective of a particular school of Buddhism varies widely depending on the local culture. In the traditional Pāli Canon, the Sigālovāda Sutta contains a large section which advises men on honoring their wives by remaining faithful.

In the book Disposable People: New Slavery in the Global Economy, Kevin Bales argues that in Thai Buddhism, women are viewed as naturally inferior to men, and that Buddha told his disciples that women were "impure, carnal, and corrupting." This is also supported by the belief that women cannot attain enlightenment, although this view is disputed by other Buddhist scriptures such as the Vinaya Pitaka in the Pali Canon.  The current Dalai Lama has asserted that women can attain enlightenment and function as equals to men in spiritual matters, but his branch of Buddhism is not the one practised in Thailand, which has its own particular canon of beliefs. Bales also points to the fact that ten kinds of wives are outlined in the Vinaya, or rules for monks. In the rules, the first three categories are women who can be paid for their services. In present-day Thailand, this is expressed as tolerance of prostitution by married women. Sex with prostitutes is viewed by wives as "empty sex", and thus women may allow their husbands to have meaningless sex with prostitutes rather than find a new spouse.

See also what it says about Social views in its section for "Reasons for prevalence and toleration".

So my understanding is that a married man going to a prostitute doesn't break the third precept. Please explain if this is correct or not.

Apparently you are not the only person to argue that.

It's a doctrine that seems to me to be far from the ideal I read in Samajivina Sutta: Living in Tune (AN 4.55) -- or this answer about an ideal partner.

The question may be a false dichotomy -- arguing that if "sexual conduct" isn't with "one of the 20 types of women" then it is "not misconduct" and therefore "correct" -- I am not sure that's reliable advice.

MN 22 for example suggests that advice might be a 'heresy' that's contrary to the Buddha's doctrine. Of course that sutta (as with a lot of Buddhist doctrine) is principally for monks. But maybe the doctrine (the Dhamma in the suttas) is universally true, even if the discipline (the Vinaya) is only undertaken by monks.

But even among lay-people there are "faithful" followers of the Buddha -- your not being a monk allows marriage and so on, I'm not sure it's also meant to encourage seeking sex with prostitutes.