If it’s mentioned in your termination letter and you don’t challenge it then definitely it will be a issue in future

1) Most checks focus on criminal records and verification of past employment dates, rather than the specific reason for leaving, unless the new employer contacts the previous manager directly.

2) if the reason is explicitly stated.in termination letter it may affect your future employment prospects 

It will still be possible to get another job, even if you are terminated for a data breach. But the impact depends on how the termination is recorded and handled.

Most of the Indian IT companies do not mention misconduct as the reason for

 termination to avoid legal exposure.

However, internally the 

HR records may classify the exit as Resignation or Termination or Termination for misconduct. That classification matters during background verification (BGV).

The BGV will depend on the severity of the breach of data.

If you sign any settlement avoid accepting the mention of the word misconduct in the relieving letter.

If not terminated yet then avoid admit in writing beyond what is necessary. Avoid aggressive email arguments. Try to convert termination into resignation if possible. A resignation is always easier to explain.

IT industry is practical. Unless it is fraud or criminal breach, career is not permanently destroyed.

You may better handle the situation patiently using your prudence.