Let's pretend this isn't horrible?

I am a single mom of 3 young kids. I separated from my ex last year. I had a fling, who also has a son. I'm 7 weeks pregnant unexpectedly (I'm getting a tubal after this, I know this is the consequence of my own actions. I already carry so much guilt with this, please I don't need to hear any shaming). We discussed trying to pull off some mixed family stuff and we both know it just doesn't work for us. We have completely different parenting styles and moral differences and neither of us are willing to compromise. He doesn't want to pay child support and at this point, I'm more than okay with not putting him on the birth certificate and just having this be my baby. He's accepting of the idea as well because he really didn't want another unless he was in it for the long run.

My issue is now, we get along great in MOST situations, like good friends. And the sex life is great. Is it wrong to maintain a casual relationship for the duration of the pregnancy knowing neither of us intend on making this a long term thing or co-parenting?