Ched,
The best thing that you can do is block all of your ghost followers. Ghost followers are either followers that have been inactive on Instagram for quite some time or followers that are actively content but are disengaged and choose to not like any of your posts.
---- Does it make sense to block followers that are clearly not real people? By this, I assume you mean bot accounts. Usually bot accounts will only follow you for a little while and then shortly after, unfollow you. If they remain following you, more likely than not, they will not like or comment on your posts, they will be considered a ghost- block them, or there are online services that can do it for you.
---- Does it make sense to block people who have an extremely high likelihood of not seeing your content? Instagram's algorithm is engagement based, meaning that even though someone is following 3k + accounts, their feed will only consist of posts that insta's algo thinks they would engage with. Blocking ghost followers will take care of this concern of yours as well. If they are not engaging with your account, they will get blocked and no longer be hurting your engagement rate.
-----What is the risk that you block that "spammy realtor account" and he actually likes and looks at your content? If that likelihood is low enough that the business' identity/brand will not suffer from the occasional unwarranted block? If you use a good tool, it will not accidentally block followers that are actually engaged, which leads me to your last question:
is there a tool that make this process a little less manual?
Yes, there are several out there that can make the process of ghost follower management less manual.
Cleaner App for IG: I tried using this one myself, it's kinda glitchy. The biggest problem: it blocks new followers that haven't even yet had the chance to engage with your recent posts. Also, have heard sometimes it blocks people that are engaged and have been for a while. Glitchy but the benefit, only costs a dollar.
CrowdBabble.com: This is an online service that will give you a list of all of your ghost followers. You have to go in and do all the manual blockage yourself though. Benefit: you can use your own discretion when blocking. Con: Lots of work, $50 for a list
EngagementGenie.com: This is also an online service. It can provide you with just a list of your ghosts, or block them all for you as well. Benefit: it likes the most recent post of all of your ghost followers in an attempt to get them re-engaged with your content. After a few days, it blocks all of the ghosts that remain disengaged.