Similar to others. We have always wanted to have kids, but the exact plan shifted when we discovered the concept of FIRE and realized that kids would be a huge complicating factor. It's super easy to make money and save money as DINKs, but its much less easy when you have kids, especially if, like us, you want to significantly scale back work when kids come along to prioritize time with them. We don't have kids yet but are hoping to begin trying in the next year or so.
The interaction between our plans to FIRE and have kids resulted in some changes:
1. Settling on an "optimal" timeline for adding children to our family. I originally wanted to have kids early (when I was 24-28). Then we discovered FIRE and swung 180 degrees and thought maybe we should wait until we are FIRE, which would put us at like age 35. But there were some significant downsides to waiting that long, namely the physicality of both pregnancy and caring for young children, and we really didn't want to put off if we had a choice. So we eventually decided to split the difference, and now we hope we will have our first when I'm 29.
This gives us 5 extra years of stashing cash (compared to having kids at 24), hopefully getting to 50% FI and then after kids arrive, being able to coast to our full FI number within a decade (so only putting FIRE off 5 years compared to FIREing before having children) while we both work part time or something and can share the parenting load. Or have one of us be a SAHP and the other work. But basically, we decided we wanted to do the heavy lifting of saving first, get at least halfway to FI, and then we can shift focus to the needs of our family and let our accumulated savings grow in the background. We think this is a pretty good compromise between setting ourselves up for FI vs the physical requirements of having children, which is just simply easier when you are younger.
2. The number of kids. My DH comes from a family with 6 siblings and liked having a large family. I was interested in having around 3 children myself. But the more we thought about it, life is just easier with a family of 4. Like some other posters mentioned, you can fit a family of 4 in any car, hotel room, most homes, etc. It just seems like the default in our society and honestly, default is cheaper/easier/simpler. I think we could revisit this after our second comes along and see if our family "feels complete" or not (and if not, that would override our plans because happiness is more important than saving a few dollars), but right now we are planning on 2 kids.
3. Given that we don't actually have kids yet, we are aware that nothing ever goes to plan, and these little strangers joining our family will basically be the biggest unknowns in our life. We could be infertile, our children could have disabilities, etc. The concepts of FIRE have given us a buffer to deal with any of those potential issues which I am grateful for. I am a worrywart by nature and think about well, what if we can't get pregnant? Well, because we are frugal and this matters to us, we can easily pay for fertility treatments without it hurting us. And what if children that we do have, have disabilities/etc that make life just a bit more complicated or difficult? Again, FI means that we have money to spare to throw at the problem. Therapies, equipment, healthcare, hiring additional care help, whatever--being mustachian means that we can easily make any of those happen. Or what if we cannot have biological children? Adoption is expensive and complicated. But we could easily handle the cost of that as well if that is a route we eventually go down. Basically, being mustachian means that we have the financial tools to make our vision of our complete family come true without completely financially ruining ourselves, however that comes about. And I'm really, really thankful for that "safety net".
edit:
4. Thought of another one. This whole angst DH and I have had about when/how many kids to have because doing so would really impact our ability to save for retirement, also then made me start thinking a generation ahead. When my own kids will face this exact same timing problem as well -- Time to make/save money vs time for kids (if they want them). And we decided that while DH and I will be doing the Coast FI thing, there is nothing preventing us from doing income-producing work especially after our kids grow older and more self sufficient. Specifically, what we have in mind is if we can 1) set our children up for basically guaranteed conventional retirement at age 65 by setting aside cash at their birth to compound over 6 decades to take some of that savesavesave pressure off and 2) *partially* help them pay for college (or whatever training/etc they choose to do before beginning their career) so they aren't starting quite as far behind the 8 ball as DH and I did. Taking away the biggest sources of money angst for my children in their own child-bearing years would give them a bit more freedom to make their choices--choices that maybe aren't as constrained or heavy with tradeoffs like DH and I have had to make.