The most trivial 'bans' are via DNS or App stores.
You could tell all ISP's as a condition of doing business in a Montana they must not resolve TikTok to customers in Montana. That would remove most non technical users and would probably be pretty trivial to implement.
ISPs have a mapping of customer to IP and therefore could return different DNS servers via DHCP or return different DNS responses based on ip.
You could also tell Apple, for example, to remove TikTok from all phones with a credit card in Montana.
The process of blocking could get as advanced as the Great Firewall of China.
So if you want to think about how you would do it, you would need a technical method of disabling (dns, firewall, app store, AD policy, etc) and a technical definition for state (likely billing address).
The US's policy AFAIK is to not balkanize the internet. So I think the US government's position is that soft bans, such as pushing policy to individuals phone's and devices that carry out the policy is ok, but mangling app stores or DNS is less ok. This promotes more of a bottom up ban (companies implementing it on employees) than a top down ban (the government attempting to force it in a specific way).
I do think banning TikTok on government devices and especially on military devices or enlisted people's personal devices is definitely a good idea. I would encourage you not to think of things as black and white, but as grey. Top down GFwC like approaches are quite bad, app store approaches are kinda bad, policy on phones is bad (but probably the happy medium, especially if the policy can be understood by the person who has it on their phone), and changing culture such that people won't use apps from foreign adversaries who frequently threaten to invade other countries is probably best. Creating cultures of responsibility is incredibly hard, so that means an element of force is probably merited for this particular problem.