4

What is the grammatical function of と in the sentence:

同じ心を持った人は二人いない。

3

This is a less common but distinct function of と. When number + counter + と is combined with a negation, it means "(not) even". 明鏡国語辞典 第二版 says:

⑧ 《少数量を表す語+「と」の形で、下に打ち消しを伴って》事が成立しないことや持続しないことを強調していう。わずか…それだけなのに…ない。「何をやっても三日続かない」「こんな所は五分我慢できない」

⑨ 《二つの意を表す語+「と」の形で、下に打ち消しを伴って》一つの意を強調していう。一つ[一度・一人…]だけだ。「命は二つない」「こんな失敗は二度しない」「こんな機会はまたない」

It may be better to memorize 二度と~ない, またとない and 二つとない as idioms.

Related: The role of と particle in 「二度としない」

2

I am thinking 二人といない could mean "there's nobody else" or "there will never be another person", along the same lines as 二度と which means "never again".

1

と or として in this usage has the meaning "as much/many as" or "even"

so your sentence

同じ心を持った人は二人といない。

would mean something like:

There aren't even two people who feel/think the same way.

or

There aren't even as many as two people who feel/think the same.

or more naturally in English:

No two people think alike. (we simplify the idea of not even two into "no two")

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