Whenever a message is sent between 2 phone numbers for the very first time, and the contacts aren't saved, any links or media content is by default not clickable.
This is by design of WhatsApp to prevent spam, and it applies to everyone. You can try sending a message with a link to an unknown number and you will see the same result.
Hence, we include text saying "Reply to see the links" in the message body. So far we have observed that customers are intuitively doing so and after that, the links become clickable.
If the user replies and then comes back to the chat, the links become clickable. You can check once on your WhatsApp to verify this.