System.LimitException: Too many query rows: 50001 even though SOQL has LIMIT 10,000 specified

Be aware that the 50k limit is an overall per-transaction limit, and not a per-query limit. Do you have other code in your test method that makes SOQL queries? Are there at least 4 other queries with LIMIT 10000 in them? If so, that would do it. That things fail only in production, where you have more data, hints that this could be the case.

Also, since you mentioned that this is a test method: if any of the queries contributing to this are in logic to set up your test you may be able to use Test.startTest and Test.stopTest to help. Code that is run between these two methods gets a new set of limits, which means that in a scenario where exactly half your work is setup/teardown you can query 100k records instead.

For the sake of debugging note that you can check how many query rows have been used via Limits.getQueryRows();.

To get the number of remaining query rows you would do:

Integer remainingRows = Limits.getLimitQueryRows() - Limits.getQueryRows();

So you could do a dynamic query limit with that if you want to get as many rows as possible up to 10k.

Integer upperBound = Math.min(remainingRows, 10000);
List<LoginGeo> logins = Database.query('SELECT Id FROM LoginGeo LIMIT ' + upperBound');