Sql Server Standard 2014: Reindex job locked by other transactions
and we have a scheduled REINDEX maintenance job that runs every early morning at 4 am.


Wait..is that really necessary to run the reindex job every day ?. Do you even look at whether the indexes are fragmented ?. Since you said its a critical system I will take liberty of assuming the underlying storage is fast that further lowers the possibility of re-indexing everyday. Please think about it.


  Is there a way to avoid the REINDEX job to get blocked by other transactions?


If you absolutely want this, then run index maintenance during downtime or when load is relatively very very less and no DML operations are going on. You can use online index rebuild ( If you have enterprise edition) but that also takes lock and may be blocked. Plus frequently rebuilding index out dates stats more often leading to more compilations

Suggestion: Use Ola Hallengren Index rebuild solution.