No, F-droid is not "open source"
F-droid's build system entirely depends on the proprietary google SDK, which is under a proprietary license; https://f-droid.org/docs/Installing_the_Server_and_Repo_Tools/#proprietary-non-free-libraries
There are rebuilds that take the alleged source code and compile a free SDK, but F-droid doesn't use those, as inconveniently applications programmed against the proprietary SDK don't compile without modifications - so f-droid uses the proprietary google SDK instead - unfortunately the result is that all software available for download on f-droid is most likely proprietary.
https://developer.android.com/studio/terms
"3.2 You may not use this SDK to develop applications for other platforms (including non-compatible implementations of Android) or to develop another SDK."
"3.4 You may not use the SDK for any purpose not expressly permitted by the License Agreement. Except to the extent required by applicable third party licenses, you may not copy (except for backup purposes), modify, adapt, redistribute, decompile, reverse engineer, disassemble, or create derivative works of the SDK or any part of the SDK."
https://opensource.org/osd
"3. Derived Works The license must allow modifications and derived works, and must allow them to be distributed under the same terms as the license of the original software."
"6. No Discrimination Against Fields of Endeavor The license must not restrict anyone from making use of the program in a specific field of endeavor. For example, it may not restrict the program from being used in a business, or from being used for genetic research."
As always, it seems that tolerating proprietary is going to kill another project yet again - as the proprietary licenses forbids F-droid from developing or possibly even working with modified versions of Android that are "incompatibility" modified to allow unshackled installing (sideloading is propaganda - there is nothing sideways about the user installing software that want to install).