From: Rabbi Moshe Sofer
To: Rabbi Yaakov Ehrlich
The Chasam Sofer rules that allowing a bechor to enter a herd where it will naturally mate is completely permitted, as only deliberate active breeding is prohibited. Tying an identification cord on the bechor is also permitted. A kohen who received a bechor cannot declare it hefker, as an unblemished bechor is heavenly property over which the kohen has no ownership rights, and he must be compelled to care for it until it develops a blemish.
Source: Shu"t Chasam Sofer YD §305