Culture can change fast in either way, towards more children or less.
This does not mean we will be stable but rather culture matters.
For example soon as a member leaves a conservative religion stream and shifts to a more liberal streams their fertility instantly drops in one generation. Israel's government even models this in their demographics projects as the flow between religious streams of Judaism is the biggest fertility modifier in that country.
This does means in part conservatives will inherit the earth because liberal culture right now cause smaller families but this is culture. I think liberals have to fix this.
Also if a women gets an education her fertility drops and the more education the lower the fertility. This means uneducated women (for whatever reason, religious or other) will inherit the earth. If educated women tend to be those with more genetic talents, and in aggregate this may be the case, then this is quite a problematic trend long term.
I think the trends to who has fertility and who doesn't isn't great and should be a real topic of conversation. As a society currently we do not deal with this head on.