I think they called these lawyers "outside counsel", does this mean
they are not part of the same organization so (in theory) their advice
and position is objective and neutral?
Not really. The economics of the arrangement are different, but outside counsel is not more or less objective and neutral, in theory at least, than in house counsel.
Outside counsel and in house counsel owe essentially the same duties in the context of a lawyer-client relationship to the client (in this case, the union), although, in practice, outside counsel with evaluate those duties and that relationship in the context of a single one off assignment, while in house counsel will evaluate those duties with a much richer understanding of the underlying facts of a matter and the larger context in which it is playing out.
A lawyer's duty is to advance the objectives of the client, and those objective are largely within the province of the client and not the lawyer, although a lawyer has greater latitude in exercise discretion regarding the means by which this objective is achieved.
For example, a client could legitimately say that it wants to bring a lawsuit arising out of an incident it was involved in, but the lawyer would usually decide which court it was filed in, what specific legal claims were asserted, and so on.
[If] the lawyers didn't think they had a good chance to win, must the
lawyers still work to accomplish this?
There are a few boundary lines, short of resigning or withdrawing from representation when not legally or ethically required to do so, because the lawyer simply doesn't want to do it.
First, the lawyer isn't allowed to bring groundless, frivolous, or vexatious litigation, or otherwise engage in unethical conduct (e.g. fraud), even if the client wants to do so.
Second, if a lawyer with an organization as a client (like a union) believes that someone within the organization, possibly with some authority, is about to engage in illegal activity that will hurt the organization, the lawyer has a duty to speak up (internally) about this conduct and urge the client representative not to break the law, if necessary, going up as high in the management or governance of the company as necessary (e.g. up to the highest governing board or CEO) to blow the whistle on this conduct internally within the organization, and to resign if the lawyer can't otherwise avoid being involved in illegal conduct by representatives of the organization.
Third, the lawyer must counsel the client representative in a manner sufficient to make the client's decision to pursue a court of action that is unlikely to win, but is not groundless, frivolous, vexatious, or illegal, an informed decision.
But, if the client decides to go forward with a course of action or objective after making an informed decision to do so with information provided by the lawyer, the lawyer has to do his or her best to carry out the decision of the client even if it would not have been the decision that the lawyer would have made. The lawyer is still an agent of the client, carrying out the client's wishes, not an entirely independent free actor.
A member had hired a lawyer with an opposing view to the union's
lawyers. Would this other lawyer necessarily have to agree with this
view or believe there is a chance at success (e.g. proving it's
illegal discrimination to have a COVID policy in the workplace)?
Again, no. Lawyers don't have to agree personally with the positions that they take on behalf of their clients, so long as those positions are not groundless, frivolous, or vexatious litigation, and the lawyer's work does not otherwise engage in unethical conduct (e.g. fraud), it isn't improper for the lawyer to do that.
To provide some context for why these rules are the case, keep in mind that lawyers are in the business, primarily, of dealing with situations in which there are potential ambiguities or uncertainties in the law. Lawyers, judges, and courts recognize that the law and language are pliable and subject to interpretation and application to a set of facts and that it is very frequently (although not always) possible to make legitimate arguments for different interpretations of it. And, it is hard, in advance, to know which of multiple different interpretations will wind up being found to be correct (with many legal issues in a case often never having those ambiguities resolved in that case because some other factor ends up making the ambiguous issues irrelevant).
Lawyers exist to make sure that every legitimate interpretation that benefits a represented party involved in an interaction to which the law applies is given fair consideration, with someone else generally making the final decision about what to do.