I've done this route many times, as I used to live in Thirsk (well, Sowerby actually) and can count with my fingers the number of times I have had to stand. It seems the shoulder peak is by far the worst (i.e. the time immediately after the off peak tickets typically become valid) for the way out. At the actual peak when only an SDR is valid on TPE it's really not too bad at all. On the way back in the evening peak the trains are busy, but as ainsworth74 says you should still get a seat. Also that first train on a Sunday is terrible - avoid where possible, it accounts for roughly half of my standing on that section of the line.
As for Newcastle bound trains, yes they're packed but none of them stop at Thirsk in the evening peak anymore, at least they didn't last time I checked, the Middlesbrough ones empty out significantly at York. It's worth noting that unlike from Harrogate, the trains from Thirsk are fully reservable, so if you know which service you will be getting back you could always make a reservation, but I really can't see this being necessary.
Grand Central wise, this first service out can be rather busy, but unless there's a significant event on or something in York it's not too bad. You usually get a seat. The departure just before 7pm from York almost always gives you a seat.
