TL;DR:
Islam.SE's traffic is high and growing rapidly. We might even overtake Christianity.SE in the near future.
We can expect a large Ramadan spike in traffic.
Unlike Christianity.SE, most of Islam.SE's traffic comes from outside the US.
Our per-day rate of questions is higher than at most points throughout Islam.SE history, and increasing (a key indicator of when a site is ready to graduate).
Over time
Summary: Traffic to Islam.SE has is growing at a rapidly increasing rate. We can expect a big spike during the upcoming Ramadan.
This plot was generated from the Site Analytics data, but it's also accessible from QuantCast. It plots the site's traffic (measured in three ways), along with a linear regression and a 20-day moving average:
Clearly there is a massive spike surrounding Ramadan. But we also see that the site's popularity is increasing at rate that is higher than we would expect from past performance.
Vs. Christianity.SE
Summary: Islam.SE is currently around 27% less popular than Christianity.SE, but we have nearly caught up and we may overtake Christianity.SE. We have comparable "staying power" to Christianity.SE, i.e., return visits to the site occur at the roughly the same rates. Most of Islam.SE's traffic comes from outside the US.
The number of uniques during the week 22-28 April given by QuantCast is given below:
Islam.SE Christianity.SE Judaism.SE
US 20226 89442 17347
Rest of World 85819 45486 8731
Total 106045 134928 26078
vs. Islam.SE (+27%) (-75%)
I took week-long traffic samples from QuantCast to compare both Islam.SE and Christianity.SE. I took samples from time periods just before Ramadan.
Islam.SE Christianity.SE
uniques visits stay uniques visits stay
2013 May 28-Jun 3 16597 19270 1.16 May 29-Jun 4 27001 32234 1.19
2014 May 21-May 27 39650 (+139%) 43886 1.11 May 23-May 29 77808 (+218%) 85798 1.00
2015 May 10-May 16 64910 (+64%) 71806 1.11 May 8-May 14 127529 (+49%) 142079 1.11
2016 Apr 27-May 3 69137 (+7%) 76521 1.11 Apr 27-May 3 121571 (-5%) 135172 1.11
2017 Apr 15-Apr 21 110562 (+60%) 122047 1.10 Apr 16-Apr 22 161370 (+33%) 178509 1.11
Where stay := uniques / visits
is intended to measure the "staying power" of the site, i.e., how many uniques keep participating.
Questions per day
Summary: While we're not consistently averaging 10+ questions a day, our per-day rate of questions is (a) higher than at most points throughout Islam.SE history, and (b) increasing.
Updating goldPseudo's answer to At what point will Islam.se grow out of the beta stage?: consistently averaging 10 or more questions a day? Here's the weekly number of questions vs. the 70-questions-per-week threshold:
Here's the same data points, but with a linear regression and 20-week moving average:
Also see:
The number of questions/answers and upvotes/downvotes per day for statistics in relation to voting
Which country has the most reputation? for geographical statistics (which should be interpreted carefully)