Piecing together a couple of different public issues lately, I think I see a trend about even-handedness. Conservatives are more likely to be equal-opportunity critics. If they don't like something, they don't like it, regardless of who is president and proposing it, and if they support it, they support it. Liberals are more likely to ignore or downplay things that prominent liberals do (I am here thinking first of Obama and Hillary, but include others, including non-politicians such as authors and celebrities). Or perhaps their sources do much of the downplaying for them before they even get the information.
It would be tempting to then conclude that conservatives are less hypocritical. That may be true, but something else is in play here. Softenings of hard edges of morality are not always self-serving; they are often relational. It may be that as a personality type, liberals are more likely to bend the rules or overlook faults because of preserving relationships, not just personal or tribal convenience. The reputation of conservatives as cruel and uncaring may come from this. Sticking to principle and enforcing standards may indeed be divisive in the short run, reducing group cohesiveness.
For those conservatives who think that if this is true it is still just fine, it is worthwhile to consider the extreme of this attitude. We have all known people who can get stuck on some small point on which they are technically right, but insisting on it creates unnecessary offense. The Congregational church I attended as a child still technically forbade card-playing at functions. It was still in the by-laws or whatever. Some kids played cards at a youth retreat away from the church one year, and some unknown person or persons made a big deal of it. I was in adult choir at the time and remember one of the tenors saying "You either have a rule or you don't. If you have it, you have to follow it."
The opposite extreme is equally disruptive, to allow anything for the sake of getting along. I suppose it would at least be consistent to always strain at gnats or swallow camels, but not both. However, it might be better to do neither.