I'm Muslim. My son is circimsised.
I am going to speak frankly so please dont be offended but i think it is important here.
Within Islam it is very important for a boy to be circumcised. It is compulsory.
In islam it is forbidden to have sex outside marriage and to conceive an illegitimate child (i feel awful using this term when thewre is a real baby involoved, please forgive me but this needed to be laid out clearly). The drinking etc, is obv disaproved off but does not come into this issue.
Your baby's father choose to have a relationship/relations with you knowing that you were not Muslim. He choose to do this without marrying you. Muslim men can marry Christian/Jewish women but the children from this marriages must be raised muslim, so a deal should be struck on marriage. This baby is a consequence of his decisions.
Having done what he has done, i dont think that the baby's father has any right to tell you what to do wrt the child. He should be extremly grateful that you are going to allow the child to be exposed to Islam at all. The child would be viewed as not to blamless in all of this, an innocent party.
I think you should put this quite clearly to the babys father. It is not your fault if his son is not circumcised, you are not muslim and not subject to shariah law and rulings. It is the fathers fault alone and he should not be bullying you into doing things as he has failed in his responsibilities. As the mother of his child he needs to show you utmost respect.