I think that there are a lot of issues that would be labeled socially liberal that are in line with republican values. If someone values individual freedom, then they can certainly make a case for the freedom for individuals to smoke pot or marry someone of the same sex. I'm actually surprised that there are not more republicans who support these types of personal freedoms.
Anyone in a political position can be dishonest. I'd say most politicians are, but some hide it better than others. As for political parties, they can also be dishonest since they often pander to their bases. A socially liberal republican is somewhat of an anomaly, but I'm sure there are some.
I think that while it is hard to know for sure whether a person is truthful or not, we can only give somebody the benefit of the doubt when it comes to such things. It doesn't mean we have to take their word for it to a tee, but we should give them a chance. A republican who is socially liberal might be a weird thing, but sometimes it depends on the person.
I do not believe that socially Liberal Republicans are truthful; for that matter, I don't believe any side of the political party is truthful. I am a Republican myself, and I just don't understand how Republicans can be socially liberal. It just doesn't make much sense to me at all.
I've never really met a socially liberal Republican, so seeing one in person would probably make me throw up red flags and I would probably question their authenticity. I believe it may be possible that they are truthfully, but I have to admit, they would be quite different compared to the normal Republican.