A bit of technical background here. Zen “monks” are ordained under a different section of the sutra canon than Buddist monks elsewhere.

In most traditions, monks are ordained following the Vinaya or discipline sutras. These include vows of celibacy.

In Japan, starting in the ninth century, they began a new form of ordination based on the bodhisattva vow. Saichō was responsible for starting this tradition of basing it on the bohisattva vow. In this tradition, they don't take a vow of celibacy, so can get married, and some do. For the history see A Brief History of the Buddhist Precepts in Medieval Japan

For another view on it:

"The Buddhist monk Saichô (767-822) dared to abrogate the multitude of traditional small precepts in favour of the sole precept to «awaken to the fundamental one-mind of Mahayana. He established a ceremony for the taking of this precept and built a Mahayana ordination platform for the purpose on Mount Hiei near Kyoto. Since then, various branches of Japanese Buddhism have adhered to this. But Zen, following in the steps of its Chinese tradition, upheld an original structure of mutual complementarity of the monastic and secular communities and thus did not completely give way to lay Buddhism. Although this was a Contradictory compromise of a kind that is again different from that of Southeast Asian Buddhism, one can say that the realization of this kind of contradiction bears potential for the future. However, it also proved to be a cause for confusion in monastic Japanese Buddhism.”

the View of a Zen Monk from Japan

There are other traditions of Buddhism that base the ordination on the bodhisattva vows. Especially Thích Nhất Hạnh with his "order of interbeing". But his monks and nuns are celibate.

I don't know much about this subject. but in a general way, why it’s permitted in Zen Buddhism is because it's based on the Mahayana and the bodhisattva vow, rather than the Vinaya, and then also, the focus is on awakening to the true nature of mind as well. So the complexity of the Vinaya is replaced by a vow basically to wake up :).

In any of the other traditions, a monk or nun can give up their vows at any time, and it is a simple process. They just need to say that they are giving up their robes to anyone of sound mind able to understand what they are saying. After that they can get married, but would no longer be a monk or nun,

And in all the traditions you can be a Buddhist and be married or in a sexual relationship (depending on the traditions of your country / society). There are lay vows you can take as a Buddhist also if you want to take on some disciplines - including vows of not engaging in sexual misconduct - which is mainly to do with expectations, not to hurt others by cheating, or by dealing with them in ways that hurt them or others around you because of cultural expectations.

However Zen Buddhism is rather unusual amongst monastic orders - in any religion I think - with this approach of permitting monks and nuns to be in relationships or married.