If you mean search filters like taxon, place, data quality, etc, then just bookmark the URL after you’ve added all the filters you like. Map zoom lock and Suggestions source, though, need to be reset after you refresh or load a new Identify page.
I personally keep a pinned tab of the Identify page the way I like it and refresh it once a day because the token expires after 24 hours of loading the Identify page.
For more about search filters in general, check out: https://forum.inaturalist.org/t/how-to-use-inaturalists-search-urls-wiki-part-1-of-2/63