I estimate that about 20% of non-Hispanic white Americans are both conservative and highly religious (defined as those who attend religious services weekly or almost every week and for whom religion is important in their daily life) and thus are, broadly speaking, the "religious right." By contrast, only 4% of non-Hispanic white Americans are both liberal and highly religious, or the group that would constitute the "religious left." More broadly, 52% of white conservatives are highly religious, compared with only 16% of white liberals.
In short, the potential for political activation of highly religious white voters -- most importantly in reference to the looming 2020 presidential election -- appears significantly higher on the right side of the ideological spectrum than on the left.
What about the influence of the religious left within the Democratic Party? Here again, the potential impact of religion for candidates seeking their party's nomination appears lower than is the case in the Republican Party. My estimate is that about 23% of white Democrats are highly religious. The majority of these highly religious white Democrats are ideologically moderate and conservative, which wouldn't fit the definition of a classic "religious left." (Only 9% of white Democrats are highly religious and liberal -- the description, it appears to me, that would best fit Buttigieg.) This suggests that Democratic candidates seeking to activate support among highly religious white members of their party would need to move more to the center of the ideological spectrum.
By contrast, 51% of white Republicans are highly religious, and 40% are highly religious and conservative, the analog to the religious right.
Blacks, who constitute over a fifth of all Democrats, will play a key role in candidate selection in several early primary states and can be a significant factor in the general election in key states. Black Democrats are much more likely to be highly religious than white Democrats are, and black Democrats are also much more likely to be ideologically moderate or conservative. This again leaves a liberal candidate like Buttigieg in a tough position if he attempts to emphasize his personal religiosity in an effort to gain black support