Steps to reproduce the issue

For com_contact enable modern routing:

Create contact categories with subcategories like:

• Category 1
  -- Subcategory 1
  

Add a contact (just with email-address) to "Subcategory 1"
Create a menu item "List all Contact Categories" or "List contacts in a category"
Chose category "Category 1"

Go to homepage, select menu "Contacts", open contact form, try to send email through form.

Expected result

Email message sent
Show contact again

Actual result

Email message is sent (in the background)
websites gives you "404 invalid URL"

System information (as much as possible)

Joomla 3.9.18
PHP 7.3

Additional comments

With routing in "legacy" mode, it works.