The fuideline stipulates that owners basically evacuate along with their pets to a safe place, *while* requiring owners to be considerate of other evacuees who do not like animals.

この文章のwhileについてですが、これを省略せずに書いたら、

The fuideline stipulates that owners basically evacuate along with their pets to a safe place, *while　they are* requiring owners to be considerate of other evacuees who do not like animals.
になると思うのですが、これであってますか？
また、これを日本語訳したらどのようになるのでしょうか？

See a translation

@kochashiba580512
do you mean "guideline"? ガイドライン言うつもりでしたか

while requiring は正しいです。while は事の状態を参照?するのです。
"while" is in reference to the situation of the guideline.

"they are" はひとの話するので,違います。"they are" would be talking about people, not the guideline itself, so it becomes wrong to use they are.

hope i explained it well

The guideline stipulates that owners basically evacuate along with their pets to a safe place, while requiring *them* to be considerate of other evacuees who do not like animals.

"owners" は最初もう言ってるし,2回目は "them" になります。