This is a "brittle" option, but I was able to get this to work by using the ArcGIS Online Assistant and editing the app's JSON.
In the JSON editor, under the Data tab, add the line
"locationEnabled": false,
under searchConfiguration (partial example below)
"disableScroll": true,
"search": true,
"searchConfiguration": {
"locationEnabled": false,
"sources": [
{
"displayField": "title_formatted",
The problem with this method is that if you go back into the Instant App's configuration and re-publish it your JSON edits will be overwritten. So you need to go back in and re-add the locationEnabled: false line every time you make any further updates to your app.