Grammatically correct but nuances are different.
I pointed AT my cat and told them that IT IS a cat, but they didn't believe me.
Using past tense can mean, that the cat is now no longer a cat. Perhaps, it is magical and turned into something else or that it is now dead.
Same reasoning for the rest of the sentences...
this person was a doctor --> this means that he may have retired, stripped of his licence etc. You should use present tense to indicate that he is still a doctor.
Use present tense to indicate that it is still a perceived fact regardless whether the situation was in the past.
In the old days, people believed that the earth IS flat. -- a fact, even though their thinking is wrong.
In this case, you can also use past tense, ... WAS flat -- here you are telling that in the old days, people believed that it was flat but no longer now.