とは言(い)えThough, Although (I admit that), Be that as it may, Nonetheless

These are both formal/written-style expressions that have the same fundamental meaning of 'even if one says'. In practice, both are used as a literary way to say 'although’, even if there is no explicit intention of quoting something that was said, e.g. ここは治安がいい(といえども・とはいえ)油断してはいけない ('Even though it's safe here, you mustn't be careless.').

Both show concession, but differ in nuance. にせよ・にしろ makes a strong assertion that something holds regardless, as in 結果が悪いにしろ挑戦するべきだ (Even if the result is bad, you should try). とはいえ concedes a point but softens with that said, as in 難しいとはいえ不可能ではない (While it may be difficult, it’s not impossible).

にしろ～にしろ lists alternatives where the outcome stays the same, as in 成功するにしろ失敗するにしろ挑戦する価値がある (Whether you succeed or fail, it’s worth trying). とはいえ acknowledges something but introduces a contrasting fact, as in 難しいとはいえ不可能ではない (That said, it’s not impossible).

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.').

とはいえ and であれ are similar in that they both express a sort of contrast, but 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.'). Though they can overlap in some cases, であれ 'even'/'no matter' is often used together with question words, e.g. 理由は何であれ 'no matter the reason', while とはいえ cannot be used this way.