Board solidarity means that a decision taken in proper form by the board is a decision of all board members. You don't get to behave as if it hadn't happened, or criticise it to outsiders, or keep agitating outside the board for your own proposition.
This can often be difficult, because boards can take decisions that you may not want to be associated with, or decisions that go against the opinions, or even the interests, of other groups - some of which groups can be among those electing members to the board. Even there, though, you're not supposed to go back to your constituents and badmouth the board's decision. As best you can, you're supposed to defend it, showing your people why it was taken and what it actually means.
If you can't defend the actions of your board at all - if you think they're utterly wrong - and if there's no chance of winning your colleagues round, then you may have to consider resigning.
An incorporated association is in the eyes of the law a legal person - but only one legal person, which means that it can only have one opinion at a time.
A board member may, of course, continue to press their views within the board if they feel there is a chance of having the decision overturned, unless there are provisions in the standing orders to limit their rights in this area (some organisations forbid motions to revoke previous motions until a certain period of months or number of meetings has elapsed).