This is really not going to affect most tourists, particularly if you plan to stay within the city of SF or rent a vehicle for travel outside the city. The only major downside will be lack of public transit to OAK and SFO airports. In the case of SFO, you can get a pretty cheap supershuttle and cabs are @ $40 to downtown, so for a family of 4 you won't lose sleep. OAK is a bit more pricey from the city.

Of course there is also the traffic issue, the bridge to Oakland will be jammed pretty bad during rush hour (though traffic is usually lighter in the summers).

But compared with a tube strike in London or Paris, this won't be a big deal for tourists trying to navigate the sights in the city as most rarely use bart within the city.