Chairman Mao and his close followers always stressed a certain point when it came to uniting all the forces than can be united to fight your enemy. They constantly wrote and spoke of the need to resist both leftist and rightist tendencies when it came to figuring who can be united with and who can not be.
To be a leftist in this sense meant to isolate yourself from potential ally's. To not unite with someone because they were not as radical as you or because they were not willing to push the issues to the same extreme that you were willing to. To look at a moderate communist and call him reactionary and struggle against him because he is not as radical as you is another example of this leftist thinking.
I have been guilty of leftist thinking and actions before and it is something I constantly self-criticize and try to improve about myself.
To relate it to today; many groups will not unite over what is in the objective realm of the real world meaningless line issues. I personally have been attacked as a reactionary imperialist supporter by MList simply because I view the USSR after a certain point as imperialist (I see no reason to call them social or red imperialist because imperialism is imperialism). Those individuals refuse to unite with me even though we agree on 80% of everything. This an example of leftist thinking and action.
Leftist thinking is hurtful to our goals as communist (as is rightist but I'll get to that). It stops us from uniting with the other progressive forces to fight whatever is being fought at that time. It isolates us to the extent that our voice is irrelevant and too small to make a noise. It also isolates us to the viewing public and the masses as a whole. How can we be taken seriously by the masses if they see us willing to split with fellow communist over the most trivial things?
To be a rightist in this sense is to unite with forces that should not be united with. To be more blunt it is the idea that we should "unite with everyone" regardless of what is going on in the struggle at that time. An example of this is the communist parties who's members took part in the Obama election under the guise that "they were working with the masses and that is where the masses were". This is very dangerous because while the group maybe participating with masses of people they are pushing the masses towards a reactionary idea and mind set. It gives a communist a false sense of accomplishing something when really they will just be advancing a reactionary line.
But I must state that these leftist and rightist ideas must be decided and combated on an issue to issue basis. For example; uniting with liberals to advance propaganda for universal health care is okay and should be done. But to campaign with liberals for liberal candidates (no matter their party) is a rightist line and should be halted at all cost!
In short conclusion we should be uniting with all of those WHO CAN BE UNITED WITH. However, we should not be uniting with forces that should not be united with. Communist should be constantly reviewing their situations and doing what they can to further advance and advocate communist ideas. If who you are working with is compromising that goal you are probably using a rightist line. If you are not accomplishing anything because you are refusing to unite with other radicals then you are probably advocating a leftist line.
(I decided to leave names of ORGs out of this post because it is really up to the individuals of a party or organization to combat these two extremes and find the correct allies to unite with and I didn't want members of those ORGs to see their groups name and stop reading the article because they viewed it as critical. Which is something that the left seems allergic to doing or hearing about their groups.)