Thankfully I didn’t need to believe a poster saying Japanese people don’t take infants into restaurants as I have plenty of direct experience to contradict this “truth”.
And contrary to much of the received wisdom (as well as my own assumptions back then) the most popular kind of restaurant selected for meet and greets with Japanese friends and their infants for us with ours was in izakaya. Turns out there are lots of infants eating out that other diners have no idea are there in private tatami rooms.
There are quite a few threads in this forum about dining out with babies and toddlers, the kind of room often preferred by Japanese families for taking out infants is called a koshitsu. If you use this as a search term you’ll find lots of feedback. Yes, there are some genuine barriers, but not very many, no need to accept or create non-existent kinds. I have VERY strong feelings about the importance of exposing young children to good food.
This is a list from tablelog of restaurants in Tokyo with private tatami rooms that accept children
東京の子連れでいける個室のあるお店
https://tabelog.com/tokyo/rstLst/cond15-04-00/
As well as translation tools, you can copy and paste the address of anywhere suitable into google maps and look at reviews in English there.
Use this for a focus on Shinjuku
https://tabelog.com/tokyo/A1304/A130...ond15-04-00/1/
and these search results for Shibuya
https://tabelog.com/tokyo/A1303/A130.../cond15-04-00/
and whilst I’m at it, this covers Ginza
https://tabelog.com/tokyo/A1301/A130...ond15-04-00/1/