No you cannot get aids from touching toilet handles or from sitting on toilet seats.
The aids virus is unable to live very long on the toilet handles or toilet seats so while the toilet seat or toilet handle may have the aids virus on it it can only live for a short time before it dies.
So even when you touch the toilet handle or sit on the toilet seat you won't be able to get any aids from it.
Also if you do touch the toilet handle and it has aids to get infected from touching the toilet handle you would have to insert your finger into your vagina or anus to get infected with the aids virus.
Simply touching the toilet handle would not get you infected with aids.
It's still a good idea to wash your hands though with hot soapy water after using both public toilets and your home toilet because of germs.
But you will not get aids from toilet handles or toilet seats but still they contain germs that could make you sick in other ways so wash your hands.