One of the worst things that can happen to your issue is that it becomes politicised i.e. one political side decides to take a stand on it and the other side takes the opposite position in response.
Plenty of issues don’t actually neatly fit the right-left divide. Frankly, they’re too complex to be easily compartmentalised (I’ve had a rant about this before here) and as such political parties or groups don’t have a clear position on them. But that doesn’t matter to cheeky politicians: when they’ve decided that they can score a win with their constituents, they’ll take a stand on an issue. They may then carry the rest of their party with them and make it very hard for you as a campaigner to get your point across, no matter how solid your arguments may be, because positions have been entrenched on the left-right axis. You’ve lost control: your issue may now fall prey to the whims of political skirmishes rather than develop through a process governed by reality and logic.
So what do you do? Hope for the best (!) and monitor very carefully so you know when and how politicisation might happen before it actually does. And make sure you have a contingency plan.
Plus don’t accelerate the process yourself. If you’re a key player on your issue, don’t tick off one side or the other if you can avoid it. How? Approach your issue from both liberal (in the American sense of the word) and conservative angles; gratify the values of both your centre-right and centre-left audiences. Sounds odd, but it actually works on a wide range of issues e.g. your manufacturing process might both be great for profit margins and will employ people in a marginalised community; your new product might have been invented by an entrepreneur who benefited from a tax break and have a low carbon footprint.
And if your issue still becomes politicised? Then the contingency plan mentioned above may become easier to implement because your relatively neutral position so far may ensure more balanced treatment than you might otherwise expect.