Works for me as expected:
C:\pwb\GIT\core>pwb replace -page:MyPage "{{MyFirstTemplate|field1=MyText|field2=MyText}}" "{{MySecondTemplate|field3=MyNewText}}" -site:wikipedia:test -simulate
The summary message for the command line replacements will be something like:
Bot: Automated text replacement (-{{MyFirstTemplate|field1=MyText|field2=MyText}} +{{MySecondTemplate|field3=MyNewText}})
Press Enter to use this automatic message, or enter a description of the changes your bot will make: Retrieving 1 pages from wikipedia:test.
>>> MyPage <<< @@ -6 +6 @@ - {{MyFirstTemplate|field1=MyText|field2=MyText}} + {{MySecondTemplate|field3=MyNewText}}
Do you want to accept these changes? ([y]es, [N]o, [e]dit original, edit [l]atest, open in [b]rowser, [m]ore context, [a]ll, [q]uit):
Note: There is no -regex option activated and the source string must match the text, see https://test.wikipedia.org/w/index.php?title=MyPage&action=edit