Do mainline Protestant seminaries in the United States involve rigorous study of Hebrew and Greek?

Nowhere near as rigorous as evangelical colleges. To compare colleges it makes sense to consider the MDiv because it is meant to be internationally comparable. But as we'll see, that's not really true.

As a baseline, I'll explain the MDiv program of the Australian College of Theology, a consortium of evangelical colleges, and also what I studied. In an MDiv at one of the ACT colleges you'll study 24 units/subjects (6 semesters, 4 units per semester. If you want to look at the details of that page, then it will help to know that each unit is 12 credit points.) Of those 24 units you are required to take 4 units for the OT and NT introductions, and then at least 6 OT/NT book exegesis units (8 NT/OT exegesis units will typically be offered during a student's time, and many will do all 8). This means that at least 42% of the units in a MDiv are directly studying the Bible. If you take all 8 exegesis units then that will be 50%.

But not all of those are in the Biblical languages. You are required to take 2 languages units (either Hebrew or Greek), and then to take 2 of OT/NT units in the original languages, so at a minimum 17% of your degree would be in the Biblical languages. It is common, especially for those who want to go into fulltime ministry, to do Greek in first year, and then 4 NT units in Greek, so that 25% of the whole is in Greek. Those who choose to also study Hebrew typically start learning Hebrew in their second year. If they only do a three year program that means they can only do 2 OT units in Hebrew, but if they do a combined four year MDiv/GradDipDiv program they could possibly arrange their schedule to do all 4 OT units in Hebrew. Someone who does that would have done 12 units in original languages out of a total of 32 units, or 38%.

But how rigorous is it? These aren't easy subjects - they're hard and take a lot of work, as I can tell you from experience! But they don't turn their students into fluent readers of Greek or Hebrew. I believe they are best for exposing students to the weirdness of the Biblical texts, which is often hidden by translation. Studying the original languages will also make you ask good questions of the texts, but it won't always allow you to answer those questions. To become an expert in the Biblical languages requires much more study than you can do in a 3 or 4 year degree.

For comparison, the Southern Baptist Theological Seminary MDiv is 88 credits, which include the required Biblical introduction units, as well as both Greek and Hebrew languages and exegesis. All up you'd be doing at least 24% on exegesis and languages, with some "concentrations" doing more.

The Westminster Theological Seminary MDiv is 111 credits, of which 18 are in Biblical languages, and 32 in Biblical studies, 45% of the whole. That's much more in line with the ACT MDiv.

It's interesting to me that the ACT MDiv seems more "theory" based (Biblical studies, theology, church history) than even these evangelical US colleges. Things like apologetics, counselling, mission aren't required (but are commonly taken as electives), while something like church leadership might only be offered as a non-accredited course. These US colleges seem to offer a broader and more practical MDiv program, whereas the ACT goes deeper into the theory side, with the expectation that many of the applied aspects of ministry will be taught on-the-job. Different approaches to formal theological education, but not right-or-wrong.

So how do the mainline colleges compare?

The Princeton Theological Seminary's MDiv program is 78 credits, of which only 9 are required to be in Biblical studies, a measly 12%. It sounds like you are only required to take one non-introductory exegesis unit. Students are encouraged but not required to take Biblical language units or exegetical units.

If you did the Anglican Studies MDiv at Union you would only be doing 11/78 credits in Bible, 14%. I can't see if you have to do any Biblical languages, but it seems unlikely if you're only doing that many credits in Biblical studies.

The Pittsburgh Theological Seminary MDiv is 81 credits, of which it looks like about 18 are required to be in Biblical studies, 22%. I'm not certain, but it looks like you may be required to study the Biblical languages, but as you only begin doing that in the summer term of year 2, there may be less opportunities to take exegesis units in the original languages. The schedule has a lot of spaces for electives, so typical students may end up doing more exegesis units.

Of the three seminaries you listed, Pittsburgh looks to have the biggest focus on both Biblical studies and original languages, though neither to the extent of an evangelical college.