replication – ERROR: Too many connectioons

I’m new to mysql. So, sorry if you find it an easy/silly question.

I have a quick question since I encountered a strange scenario. I want to make sure does it actually happens or did I do the right thing.

I was taking backup of a table from a prod replica and what I found that after some time it locked production master database table. We started getting ‘Too many connections’ error on live. I checked mysql documentation for this and found: That you should stop replication before starting the dump from replica to ensure that the dump contains the consistent set of data.

https://dev.mysql.com/doc/mysql-replication-excerpt/5.7/en/replication-solutions-backups-mysqldump.html

But, One thing I’m unable to get that yeah..from documentation I can conclude it’s good practice to stop. But, nowhere it’s being mentioned in the way that ‘you have to stop the replication otherwise – it can make your master unreachable. Did anyone face the same issue?

Also, one more thing – I couldn’t get- dump operation always make schema level lock -not to lock the whole table. So, how could this happen.

Thanks for any advice/suggestion/reason in advance!