Why is Neanderthal pronounced with a /t/ sound instead of a /th/ sound?
Although the word can be pronounced both ways, very often its German origin is honoured and it's pronounced the German way, where -th- is pronounced as -t-. Note that the word has four syllables, with the initial e separated from the a immediately following
[ne 'an deə tal].
It's a German word meaning Neander Valley, the valley where the Neander River runs, and it's where Homo neanderthalensis was discovered.
You may even find it spelled Neandertal, which is the modern German spelling.
True, the German pronunciation is T, not TH. However, since the word was adopted into English first as a scientific term, then more generally, when the spelling was still TH (it's spelled Neandertal in modern German) it is perfectly acceptable to say the TH pronunciation is appropriate for the pre-modern human species specifically. Likewise it's preferable to say KRO MAG NON (Cro-Magnon) instead of KRO MAN YON. The former is not the French pronunciation, but if you are not speaking French it is best to stick to English pronunciations with words that have been long-adopted into English.