Question Related to Unregistered Vender

GST Registration Doubt 

We avail service and goods from various unregistered vendors. Few have crossed a turnover of more than 40 lacs in the current FY and are not registering in GST. Though we are insisting they register in GST they do not consider the request. 

In such a case, can we continue doing business without GST registration? Will it create any problems for us? 

Please note we don't have any other option, hence asking. Please clarify.