I had this issue. This is how you fix it.
The reason your site works on mobile but sometimes not on wifi has to do with nameservers.
These are the steps to solve this.
1: Ask shopify to check if your domain is set correctly. CNAMES, ect. (use top domains if you can. subdomains get trickier.)
2: Once that is all set, go to where you bought your domain, and have them look at your problem. (see if you can chat, call and email and have your site settings on a different tab or window to follow along)
///explaination of 2
2.1 When setting your nameservers on some sites, you get to use the domain provider’s nameservers or the ones you provide.
2.1.1 Sometimes they get reset and take time to propagate (different internet service providers use different name servers. When they can’t find your site on their default name servers, you get a page not found or a similar error page.)
2.1.2 You can manually cycle through this on your browser settings like I did, but the page will appear and disappear unpredictably. It’s a waste of time, don’t do it.
2.1.3 Name servers refresh at different intervals and when they do, sometimes your site cannot be found until the changes have been updated throughout the internet. (service providers have name servers and the different update times leads to say mobile being up while sometimes wifi is down. You won’t notice until you try different access points like you did, or say, try accessing it on a public wifi ect)
//end of expaination of 2
3:Your domain provider (where you registered your website name) will ask you if it’s ok to use their name servers.
4: Say yes.
5: You’re done, your site should load everywhere now.
6: If something’s still not right, repeat steps 1 and 3.