I have written a custom code (a function to remove the default blue background on the text field) in Adobe Acrobat.
Everything works great when I open the pdf file in Adobe Acrobat. However, the custom code is not recognized when I open the pdf file in a browser.
Is there a way to make the pdf file supportable with both Acrobat and the browser?
No
Pdf viewers do not need to run ECMAScript code as it is commonly used for exploits. Also the historic default for acroforms FDF display is pale blue or occasionally red so you need to rewrite all viewers or ask their maintainers to do so.
Results can vary considerably this self adjusting old form cannot work
using a non blue field colour usually indicates the form field cannot be actioned