An alliance is based on a shared goal, maybe multiple goals. Two given allies might not even like each other, and that does not affect commitment toward the shared goal.
What happens when two allies have one shared goal and many contrary goals?
This is permitted in the theory of alliances, and even observed in history. For example, book publishers are adversaries in terms of controlling market share, but they are allies in undermining copyright law. The fact that they are competitors in the sale of books in no way weakens their reliability in the fight against the expiration of copyright.
A more dramatic example is that of African-American politicians who are members of the Republican Party and who are allies of other Republican politicians. They might share the goal of legislation to impose on everyone restrictions dictated by their common religion, but those black politicians certainly cannot share the goal of white nationalism. Nevertheless, each victory of the Republican party erodes the citizenship of all black Americans. The explanation? Those black politicians must have prioritised their religion over their citizenship.
What About Nazis?
Now consider the thornier problem of Nazis in the environmental movement. Is it acceptable to risk normalizing national socialism in the name of protecting the environment?
It is important to remember that normalization works in two directions, not one, and one direction is actually a goal. It has long been a wish of mainstream society that nazis might have other uses for their time than administrating hatred. Why would environmentalism not be a worthy alternative?
There is, of course, a threat of influence running the opposite direction: If Nazis are seen defending reasonable causes, then they might have other reasonable things to say. Note that this has already happened. Nazis have denounced pedophilia very strongly and they have called for strengthened protections for children. This has not had a strong effect on their acceptability. In fact, most of the penetration of right-wing nationalist ideas come from parties and individuals who are careful to not present themselves as nazis, like members of the American Republican Party and the German Alternative für Deutschland. In other words, the worst has already happened; it is merely a test of civilization to deal with such influences, regardless of whether any uniforms are worn.
Religion is another example of a threat that has already been played out. There are religions which have promoted and practiced torture and execution. At least one modern religion considers sacred a text which authorises slavery and provides helpful tips on owning slaves. This same religion has a shocking history of pedophilia and sexual abuse, and has gone to great lengths to protect the perpetrators.
Is it in society’s interest to marginalize such groups? If it is, that is a decision which has not been made. And yet, no Western society is drifting toward re-instituting slavery or legalising pedophilia. The reason? Civilization has decisively outlawed these practices and it is now impossible to promote the ideas without appearing preposterous or criminal.
Every example of nazi extremism is subject to the same censure, if only society should insist upon it. Civilization can and has dealt with extremism. It is indeed one of the jobs of civilization to limit the market of ideas to that in which everyone can consistently participate.