I'm really surprised with the glooly/pessimistic/depressing things people are saying here. I don't agree with the general point of view of people so far.
To avoid any confution let's be clear, Guitar and therefor guitar players are more common, better known and therefor more influencial in popular western music, period (and there is nothing wrong with that). But also, let's be clear that "normal people" doesn't know $h&t about music in general, a lot of people doesn't even pay attention to it, they listen it on the radio, a party and that's it. The you have another piece of the population that likes music but they listen to whatever companies are selling that day. And then you have people that really likes music some becuase they are fans fo a band of artist likebelonging to a tribe. Most of those (and I'm not judging anyone here, everyone is free to live the way they want and enjoy things the way they want) are not even aware of the amount of instruments and variety of things there are, not only the bass.
I rember once I was on the line to buy tickets to a concert on a theatre and there was this very old lady waiting to buy tickets as well, sunddenly a guy with a double bassarrives (also to buy tickets) with his behemot gig bag. The old lady, very interested, asked him if that was a saxophone....
Now, I'm not bashing on the old lady or laughing of her, they reality is, people usually doesn't know, and that's it, the same way many of us are abosolutely ignorants on many many topics. But is not jsut the bass, is all of the isntruments. Yes, electric guitar is, today, the most popular instrument, therefor, people know them better. Then, drums are quite easy to identify, but all the others... people just doesn't know.
But when we get to the other people (always tlaking non-musicians) that really likes music and enjoys it, well, those usually know, those know instruments by ther names, those know who the bass player is in that record, and who the clarinet player is in that other one. I have met plenty of people that never in their life put hands on an instrument that were well aware of the roles of each one on the band.
Going back to the main subject of the thread, I would say the simple answer is no, guitar playes are more influential than bass players in general. But if you want to go deeper, it really depends.
On classical music, guitar was a very mistreated instrument for a long time, and even today, piano players are way more influential than guitar players. On Jazz the title could be more disputed, and although there are amazing jazz guitar players, again, keys I think have more influence. And on Funk, for example, bass players have the lead if you ask me.
Even when guitar and guitar players are more infleuntial than bass and bass players, there are plenty of influential bass players out there, you may not like some of them, but people like: Sting, Steve Harris, Bootsy Colins, Geddy Lee, Jaco, Paul MacCartney, Les Claypool, Roger Waters, Ron Carter, etc, etc.
They are well known for the peoiple that enjoy the style of music they do, they are central figures on their bands and people recognice them and they influence other musicians.
And I left out of that list people like Carol Kaye (I absolutely love her), James Jemerson, Willie Dixon, Tony Levin and many many others that are legends but (I beleive) maybe not as well known.
I'm not talkiing here about the best players or anything like that, just to be clear...
As I said, yes, guitar players are way more influencial in general than any other musicians, but from there to say that only bass players cares about bass... I think is ridiculous (and I'm not trying to offend anyone, please don't take it personal)