The non-believers:

Even if a time machine gets constructed, it is still hard to proof that travelers could go back to the past, interact with it or even change it. The accepted theory on time does not allow for time travel. Past, present and future are related in a very tight, linear way, only allowing for interaction with and changing reality in the present time.

Some might argue that no event has ever changed after it happened. Each unique event occurs only ones (in its own space-time coordinates), after that the opportunity to change it has past and will not come back. Our past history time line is fixed and cannot be changed.

But what if then some kind of time machine gets invented that can broadcast messages, which can be heard as voices in your head and can be picked up by prophets of long past centuries.

People might accept that you could communicate successfully using such a device, but it would not clearly indicate and explain who the receiver really is. Proving that it is someone that lived centuries ago, might be close to the impossible.

Scientists that don't believe that the past can be changed, might feel no restraint in freely experimenting with such a broadcasting device. They might not hesitate in sending clear messages, including information that is likely to alter the future of the receiver. They might feel there is no risk that any message could backlash or have repercussions for themselves like causing alterations to their own past, present or future.

Of course they realize that they cannot use this technology to improve their own situation. At most they might think that they could help the receiver and his world to avoid problems that the senders world has experienced in the past.

It is unclear who takes the responsibility for a possible dramatic and tragic change in the future of the receiver due to wrong or bad messages.

The attitude of not believing that your actions could have serious repercussions can lead to grave consequences. If it turns out that after reckless experimenting the past did change and does affect the present of the senders then the damage could be tremendous and unreparable.