Will ATT affect Facebook website conversion campaigns?

There will be serious changes for Facebook advertisers using website conversions for measurement and/or optimization. Facebook is implementing something it calls Aggregated Event Measurement, which is its answer to Private Click Measurement, and designed to provide partial and/or modeled reporting when data is restricted, aggregated, or delayed. Facebook is also eliminating some Click-Through attribution windows, almost all View-Through attribution windows, and conversion lift measurement. Finally, Facebook is advising advertisers that audiences sourced from Pixel data will be smaller.

You will be required to verify the domains you send Facebook events from through the pixel.

Then you will need to pick only up to 8 events that can be sent. You will need to prioritize them and as far as I understand you will only see data on the last one the user did down the funnel.

Web-only campaigns/the Facebook pixel will not be impacted by ATT, since web browsers don't have access to the IDFA to begin with.  However, in response to other changes coming in the future versions of iOS (specifically Private Click Measurement), Facebook has started processing data from the Facebook pixel using Aggregated Event Measurement, which can impact web-only campaigns.

https://www.facebook.com/business/help/331612538028890?id=428636648170202