Место рождения не выбирают.
Нельзя выбрать, где родиться.
why the 2nd example uses the perfective "выбрать"
- People can not choose their birth place.
- One/you can not choose his/your birth place.
It is implied that such a choice would be a final one, for every person.
Those phrases are like mathematical proof by contradiction - they imagine some hypothetical situation - a what-if scenario - then claim this kind of situation is not possible.
Those both phrases imagine "what if" human gets born "unmarked", "unattributed", "unassigned" (as in variables).
Then, they imagine, by some action of willing choice those humans do anchor themselves, do "bound" birthplace value to themselves, after being born and raised.
Then they deny the possibility of such an imagined situation.
Like a person who is already black can not get yellow or white or red, like a person who is already French-born can not change it and became Swiss-born. As far as the choice is committed (by the person or by situation) it can no more be re-made again and again. It is a singular thing.
Now, we have to take into account the slight difference between those situations imagined by both phrases.
The first phrase -
Место рождения не выбирают - is talking about the "indeterminate quantity" of people. That is why the verb ends with
-ют - the plural form. Single would not be "indeterminate quantity", thus plural it is.
The second phrase -
Нельзя выбрать, где родиться - implies some unknown but specific addressee. "[Тебе] нельзя выбрать..." - "[you] can not choose...". Thus, it is in singular form, even there is no explicitly singular verb, like in the former case.
Multiple persons when considered all-together can (well, rather cannot here) do multiple choices - each of them is entitled only to a single one, but together their choices are many. Yet when we think about any specific person from the set, that person's choice is singular event.
The former process is kind of repetitive, not that any of those persons can repeat it, but rather "Person #1 makes choice #1, then person #2 makes choice #2, then person #3...." kind of repetition. Thus, the imperfect verb. The latter process has no "person #2" and "choice #2", thus has no repetitions, thus the perfect (committed, completed, final) verb is used.