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.

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!