Nope. This merely specifies that home.arpa is reserved for uses such as yours. It would probably be a good idea to switch to using home.arpa in case .home is ever allocated in the future, though that doesn't seem likely right now.
No, this RFC is not going to fuck that up. But some other might. Hijacking random domains is not a great idea, especially when domains cost only few bucks.
If you are the family IT bod you could register familyname.co.tld (.uk for me) or .org.uk or whatever. Then allocate each family branch their own subdomain. In the UK you are looking at around £20 per year for a .co.uk and not much more from say 1-2-3 for hosting/DNS.
Now you can get Lets Encrypt certs for routers and all sorts! Use a Dynamic DNS service if external IPs are not static.
My family may be a little unusual in that even my Dad's TV has a hostname, and so has my brother's cooker! I put in pfSense, multiple VLANs, Unifi APs and all the other good stuff. A fully meshed IPSEC VPN link up with split horizon DNS. pfSense has an ACME client and a full toybox of networking goodness. Each site config is mostly replicated to the others for backup. The office monitoring system (Icinga) has a few extra systems on it.
That lot took a couple of man days to set up. It looks after itself mostly now and just works. I've saved myself many, many hours of hassle by putting in the work ahead of time and specifying decent gear. Its probably not for everyone.
Well... maybe. You would just register the domain once (maybe `mycoolawesomehome.net`), and then you have the authority to arbitrarily decide that your printer's hostname should be `thebestprinterever.mycoolawesomehome.net`.
But now you can just use `mycoolawesome.home.arpa` without registering it.
Is this going to fuck that up?