Anyway, people assume that because children are expected to be quiet and to behave themselves, and if they are not able to do that, the parents should take them outside until they quieten down again (something which our priest refers to as “common sense”), that we are somehow “anti-children” and not pro-life.

No, we just have expectations that proper church decorum be respected.
Well, I generally agree with your position. I would just add a few things.
One is that different people have different standards as to exactly when a child should be removed. I suspect that at my parish, there is probably a very small number who would prefer that we not bring our son at all until he is older and can still perfectly still and entirely quiet for 90 minutes. There are no doubt other who don’t think like this, but who think we should remove him sooner than we do. Then, there are others who aren’t bothered by his behavior at all. I think that patience with young children, as well as with their parents should be the rule here. I think this as a parent, and I thought this way before I became a parent.
A second thing that I would add is that there can be cases where it might be necessary to removed a child from the nave to the foyer, or even entirely outside, more than once during a service. I know that with my son, it is not unusual for us to have to take him to the foyer two of three times within the same Divine Liturgy. For us, there’s really no issue with worrying about having to ask multiple people to let us out of a pew; we attend a small Eastern Catholic parish, so can always set on the end, and it’s not unusual that we have an entire pew to ourselves. However, if we were to attend a large parish where the church is generally packed, it would certainly be much less disruptive to the other people sharing a pew with us if they were to allow us to set at either end of the pew, particularly in those cases where there’s merely a preference, rather than a real need for the other person to have an aisle seat. Now I’m not saying that there’s an obligation for anyone else to do so, or that I would be angry with the other people if they refused to offer us a seat at the end. I’m just saying that it would be a much appreciated act of kindness.
Finally, I would add that some children, for reasons of their particular stage of development, for reasons of developmental disabilities, or for certain medical conditions, simply cannot, by any reasonable standard, be “expected to be quiet and behave themselves” for any more than a few moments at a time. Please take into consideration that this can being far more trying on the parents, who must live with this reality daily, than it is on the other people at Mass/Divine Liturgy. Parents in such families do not need our disapproving glances, scoldings after Mass/Divine Liturgy, unsolicited advice, or accusations that they are being selfish by bringing such children to church in the first place. They need for us to be supportive, loving, and patient with them and with their children.