I don't think it's unreasonable at all OP, dating can be complicated enough without worrying about the added complexities of having extra parties to consider.
When I was on online dating I would avoid men with children not because i dislike children (far from it) but because i was childless myself because i hadn't felt a strong enough desire to have my own children, therefore I wasn't ready to perhaps be in a situation where I had some responsibility to other people's.
BUT I was 28 so it wasn't a huge issue because the guys I was generally speaking to weren't Fathers anyway and I don't think my profile at the time was one that would attract Fathers - I was a young professional living in a house share.
As it turns out I met someone lovely who I am with now 2.5 years later. If we were to split up I may have a different view on men with children - my life is more settled, i have bought my 1st house since meeting DP and my desire to have children in my life is stronger.
So I guess that it depends on your stage of life.
I see that you are 32, I think at 32 there will still be plenty of men without children, particularly if you are looking within city areas. Maybe try something like my single friend that was always full of childless men.
I do think that you deserve to have the criteria you want and if yours is to have a childless man then I think you don't need to justify it to anyone. As long as you are realisic with yourself because as we get older we will find more people within our 'target pool' who have children. I think at 32 you will be fine - a lot of the guys I spoke to were early 30s and very few had children, I lived in a big city though, I know a lot of 30 somethings without kids because they've either focused on their career or enjoy having no responsibilities too much. Even if you don't live in a city if you widen your search area you will be fine.
I loved online dating if for no other reason it was really exciting to meet new and different people - I wish you lots of luck