Importance of the current postdoc advisor's letter in TT job search
In my view, strong letters are extremely important. You certainly don't want any letters from people interested in sabotaging you in any way. Even poorly written letters can be a setback. So can letters written by non-native speakers who may not grok the nuances of certain phrases. 

There is the concept of Damning with Faint Praise that can be absolutely deadly in a letter. It can be intentional or not, actually. 

Get letters from people who know your potential and are willing to speak for it. They need to know about your past work, of course, but people will be looking for potential and how it relates to a particular position. 

If you have any doubts about what a person might say, ask them about it, or go elsewhere. In certain situations (non-native speakers, say) you might even request that a letter writer check their letter with a neutral third party, such as a department head. This would have saved me tremendous grief long ago.