They might, but I doubt it. Especially if I made the comments in jest. "What's all that rope for?" "A lynching wink"
Home Depot (the company) will not make any effort to ban me from using their chain even if an employee did make me leave the premises. I could just go home and order it online from HomeDepot.com and have it shipped right to me.
You're sort of moving the goalposts here: when/if you have knowledge that someone is going to do something immoral, there may be an expectation to avoid supporting it. If you can't reasonably have been assumed to have knowledge of the bad thing, then there can't be an expectation to have done anything different, because you couldn't have known.
So, much as after you kick someone out of your store they could order on the home depot website, they could also just go to Lowe's and say nothing. Neither company is really to blame in that case. On the other hand, I wouldn't say that you shouldn't escalate to law enforcement if someone is threatening to go lynch someone in your presence.
Home Depot (the company) will not make any effort to ban me from using their chain even if an employee did make me leave the premises. I could just go home and order it online from HomeDepot.com and have it shipped right to me.