What is the correct grammer for this sentence?

There’s nothing wrong with either “is”. Both correspond to something singular.

I don’t believe “is” is being used incorrectly, because it implies a state of being which exists in both parts of the sentence. It just sounds redundant in this sentence. Try this:

Introducing new ideas and replacing old ones is always a highly controversial matter, especially when tension already exists between older and younger generations.

I’m thinking:

Introducing new ideas, and replacing old ones, is always highly controversial, especially when there is already tension between an older and a younger generation.

The words need to be changed around to flow correctly. Try this idea. When there is already tension between older and younger generations, replacing old ideas and bringing in new ones can be highly controversial.

Introducing new ideas and replacing old ones is always a highly controversial matter, especially when there is already tension between AN older and a younger generation.

Try this:Introducing new ideas and replacing old ones is always a highly controversial matter, given the tension between the older and younger generations.

I think this sentence is better: introducing new ideas and replacing old ones are always a highly controversial matters,especially when there are already tensions between an old and young generations.

Maybe a better structure is:

Replacing old ideas with newly introduced ones is always a highly controversial matter, especially when tension already exists between older and younger generations.

What might be throwing you off is the word “and”, or maybe it’s just the structure of the sentence itself. Hopefully the new version helps!

(…and by the way, “grammar” is the right spelling of that word.)

The second “is” doesn’t sound right…

Try re-wording the sentence to read, “…especially when tension already exists between older and younger generations.”

Which “is”?

I thinnk the first one is fine, you might try replacing the second one with “when tension already exists between older and younger generations”