であれ〜であれWhether or, Or, No matter which, In either case

Both mean whether…or…, but tone differs. にせよ・にしろ can be used in everyday speech or writing, as in 男にせよ女にせよ参加できる (Whether men or women, they can join). であれ〜であれ is more formal and academic, usually with nouns or な-adjectives, as in 貧乏であれ金持ちであれ人間は同じだ (Whether poor or rich, people are the same).

Both list alternatives meaning whether (A) or (B), with the result unchanged. にしろ～にしろ is more common and conversational, as in 雨にしろ雪にしろ試合は行う (Whether rain or snow, the game will be held). であれ〜であれ is more formal, used in writing, as in 学生であれ教師であれ責任は同じだ (Whether student or teacher, the responsibility is the same).

These are essentially the same grammar point, expressing no matter if one thing is true, the result does not change. The difference is that であれ～であれ is specifically used when comparing multiple options, e.g. 子どもであれ大人であれ 'no matter if they're a child or adult', while であれ is used with single examples, e.g. 大人であれ 'even if they're an adult' or with question expressions, e.g. 誰であれ 'no matter who it is'.

何しろ introduces reasons or explanations, like after all. であれ〜であれ presents alternatives to show the result is unaffected, as in 男であれ女であれ歓迎する (Whether man or woman, they are welcome).

とはいえ 'although (one could say)' specifically qualifies a statement by saying one thing might be true, but there is more to the matter, e.g. 日本人とはいえ、フランスで生まれ育った ('Though she may be Japanese, she was born and raised in France.'). であれ～であれ is specifically used when comparing multiple options, e.g. 日本人であれ外国人であれ、法律は守らないといけない ('No matter if you're Japanese or a foreigner, one must obey the law.').