Yes, you are allowed to licence open source software which allows for different limitations. Common open source licences you’ll see a lot of are Apache 2 which is what the Android Open Source Project uses, or GPL v2 like the Linux kernel. There are plenty of explanations online about the different licences and the limitations they impose on distribution of a piece of software.
Genuine question, is it possible for a developer of a FOSS project to enforce copyright protections or does the nature of FOSS disallow that?
Yes, you are allowed to licence open source software which allows for different limitations. Common open source licences you’ll see a lot of are Apache 2 which is what the Android Open Source Project uses, or GPL v2 like the Linux kernel. There are plenty of explanations online about the different licences and the limitations they impose on distribution of a piece of software.