It is not OK to raise a baby night owl. When my son was born my husband worked nights and did not have a drivers licence. I would drop him off and pick him up, and baby had to come with me. I would get the baby down to sleep only to put him into a car seat and drive my husband to work. Then I would try to get him to go back to sleep when we got home. No luck, we would be up all hours of the night. Then finally sleep, and the alarm would go off so I had to get up and put the baby in the car again to go pick up Daddy.
When we got home Daddy would want to play with baby. So we were up for a few hours more. Then we would all fall asleep during the day. Missing out on every thing that happens in the day, like walks and sunshine. We all ended up sleeping in the day and being up at night. Finally my husband realised this was killing us. It was to hard to be a family, do things or just live life if we slept all day and were up all night. So he ended up getting a day job when our son was about six months.
Looking back I know we missed out on a lot of things for the first year of his life. Just being up when every one else is makes a big difference on how you live your life. Staying up all night made it impossible to socialize so our son did not have a lot of contact with other kids, or other people in general. We missed out on park time, baby groups, or just getting out of the house. What do you do when you live in a small apartment and are only up at night? You are not very active, you feel isolated, you watch a lot of TV and you never get a break. It became stressful for all of us. It was not fair for us to do that to our child, or to ourselves.
It has taken years to get our son to sleep at night. He would always try and stay up as late as possible, and would fight going to bed. It took hours to get him to go down. We would start around 8 pm only to get him to sleep some time between 10 pm and 12 AM. When we did get him to go to sleep he would wake up in the middle of the night and we had to start all over again to get him to sleep. It was a hard thing to break, having a night owl baby.
I know that it is not possible for every one to have a stable day job, too many shift work jobs and night shifts. If it is possible though, give your baby a nighttime bedtime routine so they can be up with every one else and fit in with most of society. My husband was a night owl as a baby and most of his life. He could never seem to sleep at night and ended up living a life of night shifts, always struggling to fit his life schedule with daytime society. Being a night person can be lonely and difficult to balance. It is also harmful to your health and well-being. Even after years of not working nights he will end up awake all night because he feels more awake and alert at night. This is some thing he will struggle with for the rest of his life. This lifestyle is not some thing I would knowingly inflict onto a baby.