Democrats have offered to reopen TSA and FEMA but Republicans won't let this happen? Why?

Because they want to make it appear that it is Democrats fault that FEMA and TSA aren't open.

However, it is actually the Republicans keeping FEMA and TSA closed instead by their actions. 

Whereas the main problem Democrats are having is not at all with FEMA or TSA but ICE. However, the Good news is that Kristi Noem (dog and goat killer) and Corey Lewandowski (being investigated for Corruption now) are gone so hopefully ICE won't shoot anymore Americans than the 3 American citizens that they have killed so far. So, I don't see Democrats ever backing down regarding DHS until Trump protects citizens by taking away ICE masks and making them wear name tags and video Cameras all the time. So, DHS will stay closed until this happens is my best guess now.