We bought a 1 day pass for travelling around San Francisco on the bus and the cable car on MuniMobile. It worked really well until we tried to get on the 130. The driver refused to accept the day pass but couldn't explain to us why not.
I was wondering what was different about the 130, why wouldn't the driver accept the pass?
Unfortunately the San Francisco Bay Area has a number of different public transport providers, who are for the most part not at all integrated. Over recent years they have at least worked on integrating payment via "Clipper Card", however even that integration generally doesn't cover things like passes.
In your case, you purchased a "Muni" day pass, which covers any services run by Muni - including numerous buses, light rail ("metro"), cable cars, etc, that operated within the City of San Francisco.
Bus 130 is not run by Muni, nor is it a route within San Francisco. It is instead run by Golden Gate Transport, and whilst it does start in San Francisco, it ends in San Rafael around 20 miles away.
As this route is not run by Muni, it is not covered by your MUNI day pass.
San Francisco and the Bay Area are served by a confusing, often overlapping array of transit operators.
The Muni day pass allows riding on all Muni-operated buses, trains, and historic streetcars for the period of its validity; their 1-day visitor passport additionally allows riding on the cable cars. However, neither of these passes allows riding on any of the other transit services serving San Fransisco, such at BART.
Muni does not operate a bus called 130, so it would not be included in your day pass. Probably you encountered the Golden Gate Transit #130, which goes between San Francisco and San Rafael, in Marin County to the north of the city. This bus is operated by Golden Gate Transit and so you must pay a Golden Gate Transit fare to ride it. (Extra-confusingly, SamTrans, which is another operator not included in the Muni pass and which operates south of San Francisco, also runs a Route 130 which connects with Muni, though in a part of the region where tourists are less likely to accidentally run across it.)
TLDR: For regional travel, use the regional card/app Clipper. Muni has no 130; that's a Golden Gate bus that nominally does not go to San Francisco. Asterisk.
You used the city agency's app (not Clipper) to buy the city pass. That is fine, but it limits you to their vehicles only. If you wanted to unlock travel beyond the City, the Bay Area has a regional platform/card/app called Clipper. Had you bought that identical pass on Clipper, you would then have a Clipper account and have been able to tap onto any regional transit except Amtrak. (of course you would have to pay a fare, and have that pre-deposited into the Clipper system, which is notoriously slow to propagate due to its architecture pre-dating affordable cellular data, secure P2PE, and the like. They're working on it.)
Muni buses are silver and red**. However, the downtown area is like an international airport. There are many private and foreign (from outside San Francisco) bus lines provide express service from their county or other faraway place.
They are not there to provide intra-City transit. Some must traverse the city to leave it; they make intermediate "boarding only" stops for people going to their county. They tolerate and cooperate (or do not) with a sort of "hidden city ticketing" where you hop off still within the City. (though you may need to "tap off" or be charged for the farthest zone). Tourists have been known to (ab)use Golden Gate Transit for a very fast "hyperspace jump" to Fort Point (city-side foot of the bridge). Golden Gate Transit has flipped back and forth on dis/allowing this. At last report I understand they allow it because of COVID, but their local fare within San Francisco is downright punitive.
Decades ago, GG once permitted this on a Fast Pass but never on a tourist passport (not sure why; that's the perfect use). Such agreements broke apart decades ago because of the ongoing morphing of regional transit.
I hear from some a hidden gripe that the Bay Area doesn't have a single regional transit system. Feel free to line up at City Hall to sound that complaint; to get to the back of the line, take CalTrain to Morgan Hill :) But in fairness Clipper ain't terrible; it's only a problem if you want to take Amtrak or go to Rio Vista (which is closer to Sacramento than San Francisco anyway).
** Well, the surface streetcars (trams) aren't silver and red, are bedecked with historic liveries of dozens of cities which used PCC type cars. But none of those cities are close enough to be a confusion, and being rail, it's obvious they are limited by their infrastructure. And Muni passes are not valid on cable cars, except for certain specific and costly tourist passes.
In the San Francisco Bay Area there many different agencies providing public transport, including Muni, BART, Golden Gate Transit, Caltrain, etc.
The Muni Day Pass is only valid on Muni services.
The 130 bus is operated by Golden Gate Transit, so it is not included in the Day Pass.
