Arguably, a "boycott" only refers to a purchaser, not a seller to begin with. But I don't think in practice most people adhere to that distinction, which tends to melt as applied to more bilateral agreements anyway. There seem to be many boycott campaigns which urge a more broad refusal to transact with a given party -- refusing to purchase their goods and services as well as refusing to allow them access to your own goods and services.
But on face it seems to me at least that our intuitions are very different if the boycotter is buyer-side or seller-side, and I want to know if those intuitions hold.
For example: suppose John Smith refuses to buy a Sodastream because he's boycotting Israel. Many people would say "he has the right to do that", even if he's misguided. Indeed, on one level it's a bit perplexing to think through what it would mean to say he doesn't have the "right" to do that -- can he be compelled to buy a Sodastream? One Sodastream for every American, whether they want it or not?
Now imagine the reverse scenario: John Smith wants to buy a Sodastream, but Sodastream really dislikes his politics. So the company decides, unilaterally, "we won't sell to John Smith". Is that okay? Aside from some hardcore libertarians, I think this would be broadly condemned. There is an expectation that businesses which are generally marketed to the public will make their goods available to the general pubic in an open and non-discriminatory fashion.
Perhaps it's just our political sympathies driving this answer. But I'm dubious. When right-wing "Christian conservatives" tried to boycott Disney World for being too pro-gay, I thought that the boycotters were disgusting bigots, but I thought they had the "right" to express that bigotry via refusing to go to Disney World (again, what's the alternative? Mandatory Disney vacations?). But I'm not sure I would have been okay with Disney World deciding on its own to close its doors to conservative Christian families who otherwise are coming in and adhering to park rules.
The same logic applies to conservative bakers who don't want to serve gay couples -- there is an asymmetry in that the gay couple could very much say "I don't want to patronize this business", but I'm warier of the business saying "I don't want these sorts as my customer."
Another possibility is that the distinction isn't really buyer/seller, but rather individual/business (or institution). This could cover cases of solo contractors -- an artist, say -- who limit who they'll accept commissions from to those who share their values. They're "selling" art, but do we view them same as a company? On the other hand, if that artist was on Etsy and just picked certain ethnic groups or nations or religions she'd refuse to ship her wares to -- how would we view that?
I don't have a clear answer to these questions. But I do think there are some intuitive distinctions that are driving a lot of public discourse. There's a naive (dare I say) neoliberalism that treats boycotts as simple a matter of free contract -- anyone can transact (or not) with anyone they want, for any reason; the decision to refrain from buying or selling from a given person is purely a matter of individual taste expressed through the market. But I don't think that view actually is sustainable, and doesn't account for our actual views on these questions. There's a clear difference between saying "John Smith can't boycott Sodastream" and "Sodastream can't boycott John Smith", one that belies any superficial parity between buyer and seller as free contractors.