No, you don't have to purchase other carpets/rugs to satisfy their needs. Their personal aesthetic decor tastes are not your responsibility as a LL. You will not be held accountable in any legal court if your tenants chose to go that route, which would be crazy if they even would consider it.
If they are unhappy with the fact that they need carpets/rugs now and cannot have bare hardwood flooring as per the HOA, then you may wish to let them out of the lease as the other poster wrote. Make sure your rental agreement includes that paragraph about the HOA. If it doesn't make sure it does going forward and present an amendment to your current tenants.
If they simply do not like the color or design of the carpets, then boohoo for them. They have the option to buy ones that go with their style and take them with them once they move out.