Are you sure that DT is using ETag? We have multiple kuberneties environments and we've never had conflict on such header parameter. If there is such in your example, you should open support ticket. Unfortunately users are not able to define custom header params.
For me, I get this information for dev team ETag is modified as followed
On which you can see dtagent, all add data block our caching efficiency.
You can turn off the etag header usage in application configuration. Dynatrace adds it's value to etag to speed up changes in application configuration only. Unless you application configuration in Dynatrace changes,the value added is the same. Thus it won't break up things. I have only encountered problems when web request service sent empty Etag headers. That is however a bug of the monitored application.
We had an issue when application was sending Etag header with just a space character. Dynatrace added it's info and the request was cached but it should not be. The app should not pass the header without a proper value.