This problem seems to be present in any dataset but I will give an example from Stata official dataset.

Code:
use http://www.stata-press.com/data/r13/laborsup

probit fem_work fem_educ kids other_inc
margins, dydx(other_inc fem_educ kids) atmeans  post

ivprobit fem_work fem_educ kids (other_inc = male_educ)
margins, dydx(other_inc fem_educ kids male_educ) atmeans  post
If I run this, probit and margins after probit produce different coefficient and standard error, which is expected, and which is good. The fact that margins produce similar coef with LPM gives additional confidence.

However, ivprobit and margins after ivprobit produce the same coefficient and standard error. This seems highly unlikely and strange.

Why is this like this?