Also happening for us randomly. Our customer is sending an sms campaign and when she receives it, the links are not clickable. Sending to others as a test, the links are sometimes clickable. We can find no logic to when the links are clickable or not clickable.
There is no dollar sign, and the message is sent to people who have no previous text conversations with this number and it can work, or not work.
All devices tested were on either iOS 13 and iOS 14. The problem could only be reproduced on iOS14.