Question

which part of the sentence given below has an error in it
please don't indulge/ in peddling/ these offensive stereotype.​

Answer 1

this offensive stereotype

Answer 2

There are two possibilities here.  

Please don't indulge/ in peddling/ this offensive stereotype.​

Please don't indulge/ in peddling/ these offensive stereotypes.​

The main issue is singular-plural consistency.

Technically both the sentences are correct.

We use 'this' with 'stereotype' and 'these' with 'stereotypes'.  

However, when it comes down to usage, we prefer saying 'stereotypes'. Also, peddling is usually used with a plural noun, like 'peddling rumours' or 'peddling drugs'.  

Therefore, I would prefer the second option- 'these' and 'stereotypes'.