These conflicts can cause cache delays when the processes in two or more CPUs are working on the same data concurrently. There is no conflict so long as all CPUs are reading the data. Each works from its own cache copy in that case. But whenever one CPU modifies the data, all other CPUs suffer a cache miss on the next access to the same data.
In general the only way to avoid such conflicts is to separate the readers and writers in time. Arrange the program so that data is updated occasionally in a burst, then used for a longer period.