As someone who doesn't have my own kids I always look for adult-only options when it comes to hotels etc. I find having kids around me, especially young kids that scream a lot, very stressful. However, in spite of that, when I am in a public space, or on public transport, I recongnise that kids are part of life and I accept that. Regardless of my views, I have no right to enforce them on others or to expect others to behave in the ways I want them to. It is about respect. I don't want or like being around kids but I respect that others want kids and have them and that will mean babies crying, kids running around knocking things over etc. Kids are part of human life... if we get angry about that then we will be angry all the time!
That foul-mouthed passenger was just darn-right rude and inconsiderate. The swearing part was irrelevant or not depending on your attitude to swearing but IMO it was the very fact that he was inconsiderate and rude about it. If it was me then sure, I wouldn't have been happy and I might have whinged a bit to my wife when I got home but I would never have complained at the mother or the kid... they are just being a normal family. What is the mother to do... gag the kid? Babies cry even when nothing is wrong and anyone who thinks they should not are not being realistic IMO.
The fact this happen in First is also irrelevant. Consideration of others applies in all classes of travel! Having said that, I also believe that as a parent you might also recognise that people pay a lot of money for the ability to get a good rest on a flight (more space, flat bed etc) and by taking your baby into that cabin you risk ruining the experience of the entire cabin. So while I wouldn't ever complain at a mother with a crying baby I would question their consideration of the other passengers by taking the baby into that cabin in the first place. People can't get a good rest in WT/WTP most of the time because the seats don't go flat so perhaps that is the better place to take babies and that would be the more consider class for families with young kids.
The only way to ensure you have a flight untroubled by babies is to use a private charter. In fact, having looking into it previously, a shared private charter often does not cost a lot more than a standard First ticket. There are web sites that allow people to get together to share a charter flight. It sounds like that foul-mouthed passenger thought travelling First gave him the right to ignore respect of others. I find that this is not uncommon.
Perhaps there is a market for adult-only airlines or even for certain flights? I suspect there is... do a search on Google for "adult only airline"... interesting results... I'd use them! Then we'd have a genuine choice. At the moment, that choice only really exists for those with enough money to use private charters.