using MongoDB.Bson;
using MongoDB.Driver;
using MongoDB.Driver.Linq;

var settings = new MongoClientSettings { LinqProvider = LinqProvider.V3 };
var client = new MongoClient(settings);
var db = client.GetDatabase("test");
var coll = db.GetCollection<C>("coll");

var query = coll.Find(x => x.Text.StartsWith(x.Match, StringComparison.CurrentCultureIgnoreCase));
Console.WriteLine(query);

record C(ObjectId Id, string Text, string Match);

find({ "$expr" : { "$eq" : [{ "$indexOfCP" : [{ "$toLower" : "$Text" }, { "$toLower" : { "$toLower" : "$Text" } }] }, 0] } })

find({ "$expr" : { "$eq" : [{ "$indexOfCP" : [{ "$toLower" : "$Text" }, { "$toLower" : "$Match" }] }, 0] } })