To remove the Algolia Shopify app, it is recommended to first disable both Autocomplete and InstantSearch to ensure that your site functions as you'd expect without Algolia handling these aspects. Under Search Options > Search Basics you can toggle them to Disabled:
Your site should no longer utilize Algolia for its search in either the initial autocomplete dropdown, nor the search results page. Please ensure that it now functions appropriately (pending whatever changes you expect that you still need to make, of course.)
You'll then want to remove Algolia from all themes by clicking the Trash icon next to each of them. Under Search Options > Enable Algolia on a theme.
Lastly, you can delete the app entirely. Under the Shopify App Settings select Remove: