Hi there!
Google Pay: If the buttons are showing when browsing your site on some computers, it would indicate that your site is working correctly. If it weren’t then the buttons would not appear at all.
Make sure that you are browsing the site using the latest version of Google Chrome and that you are logged into a Google acccount that has a Google Wallet set up on it. If you are not logged into an account that has Google Wallet setup, the buttons will not appear.
Apple Pay: That’s correct, conflicts caused by third-party themes are a common cause of the buttons not appearing. Third-party plugins can also cause this, so another test you can try is disabling all plugins except for WooCommerce and Stripe.
There are also a few other things that you can check.
First, go to WooCommerce > Settings > Payments, then click manage for the Stripe settings. Once on the Stripe settings, enable logging. This will save the communication between your site and Stripe.
Once logging is enabled wait for about 2 hours to give your site some time to “check in” with Stripe. During that time, I’d recommend making a test purchase as well using Stripe (you do not have to use Apple Pay for the order). After that, head to WooCommerce > Status > Logs. From the drop-down menu on the right-hand side, chose the most recent Stripe log and then click view.
Read through the log to see if there are any errors. If you do the errors will help identify any issues that are happening. If you see an error but don’t understand what it means, you can share it here with us – just be sure to not include any other sensitive data from the log.