This chart on technology adoption lifecycle can also apply to ideas like veganism. Today vegetarianism is in the stage of "early adopters" and veganism is either "innovators" or maybe just going into "early adopters." Ignore the comment about twitter - it's out of date since the graph is from 2009. Twitter is now being used by the late majority.
Source:
http://www.trendsspotting.com/blog/wp-content/uploads/2009/11/early_adopters_twitter2.PNG
The key thing is that people are in each of one of these categories. What this means in practice is that if you are a "late majority" person with respect to a certain issue (or just in general) someone can say to you in 1996, look at this, it's called the internet, and the person says "I can't see a use for it, I can get books from the library when I need info, and keep in touch with people by phone. It'll never catch on and I'll never use it." The exact same person will then have set up a facebook account eventually in about 2010 when they see other friends and family have done so.
So the point is people will adopt at a given time according to how many other users there are, and not according to the underlying arguments.
I think this same curve can work in ideological arguments. Relatively more conservatives will be late majority or laggards. The exact same person who will tell you today "my body just tells me I need meat" will be mostly or entirely vegetarian as soon as 50-70% of population in their country/ social circle becomes vegetarian (were that to happen in their lifetime). They will then make some excuses to justify the contradiction with their older position, or just conveniently forget it.
Some of this is because that have insufficient intellectual ideology, both in terms of ethics (not ethical enough to not do something that is neither legal or socially unacceptable) and intelligence (not smart enough to think differently to others). And some of it is just practical. I had a mobile phone in 1998 and it was fairly useless since I only knew two other people that had one. (Although funnily enough years later everyone I tell this too seems to have a story about how they had a mobile phone in 1996.)
Bottom line: as long as vegans are only 1% or 5% of the population there are some people that will never join them. The most important step in convincing them to go vegan is to get the % of vegans/vegetarians to a much higher number, then try and convince them.
The same logic works in individual families or groups or friends. Within my (wife's) family out here in Chile, I am the first, a young niece is the second, I have an idea who might be the third, and so on. My niece (in law) would probably not be vegetarian today if it wasn't for me. And then I already have an idea of who to go for next. There are others I won't waste time on for now, but might try if I can get 1-2 others first....
But that doesn't mean that as soon as someone tells your that they voted for Theresa May, you don't bother to try and convince them to be a vegan. People can surprise you. I think it would make sense for a vegan activist, if they had a certain amount of time to target a group of 50 conservatives and 50 liberals, I would probably split that time 20/80.
Some of the conservatives that go vegan will in their own way, be innovators, within their circle and their lone veganism in the face of criticism will be more impressive than the veganism of a left wing environmentalist who is surrounded by fellow veggies left, right and centre. We need that as well, to avoid divisions, and because some conservatives will eventually turn vegan because someone at their church, within their family convinces them, not because they want to listen to what liberals are doing and be told by them.