To gauge the relative popularity of "these sort of things" in historical usage, I ran Elephind newspaper database searches for that phrase and for fifteen related expressions, representing various permutations of this/these, sort/sorts, and thing/things across the period 1800–2017.
Interruption: An important note on Elephind searches
Before discussing the results, I should observe three things about Elephind search results.
First, the results tend to tend to yield results whose numbers distribute across a bell curve, owing to a couple of factors: (1) the relative scarcity of newspapers in the databases that Elephind searches as you go back in time; and (2) the consequences of copyright restrictions on the availability of newspapers for searches as you come nearer the present. The net result of these contrary forces is that the number of newspapers searched reaches its maximum in the decade 1910–1919, and in fact peaks in 1915. (I base this conclusion on the results of an Elephind search I ran for the word the.)
Second, Elephind searches substantially more newspapers from Australia than from the United States over the full range of its coverage (1780–2017). My search for the, for example, yielded matches from 104,628,361 Australian newspapers and 42,601,972 U.S. newspapers. That's a lot of newspapers from each country, but it's a lot more from Australia. This reflects the greater accessibility of the digitized newspaper collection through Trove (the online presence of the National Library of Australia) than of the combined Library of Congress and state online newspaper collections in the United States.
Third, newspapers from Australia form an even greater majority of the searchable newspapers from 1925 forward: 47.3 million from Australia to 10.3 million from the United States, judging from my the search. That's because Australian newspapers continue to be available from Trove after 1925, where as the Library of Congress's collection from 1925 forward is not searchable at all. The main sources for U.S. newspapers from the post-1924 era are the state collections from California (3.6 million newspapers), Illinois (2.6 million), Colorado (1.0 million), and Texas (0.79 million).
So the results of an Elephind search give outsize prominence to results from Australia and from states that have searchable newspaper databases (in addition to the states already named, Pennsylvania and Virginia have searchable collections of more than 100,000 newspapers from 1925 onward; and university libraries in Missouri, New York, Ohio, Massachusetts, and Virginia do, too), and they become progressively weaker as you get closer to the present.
Having clarified what the source of my results is, I return to those results.
How usage is distributed in the Elephind results
Here is the distribution of the matches I got for the sixteen phrases that I searched for across the years 1800–2017 (with the source of the matches further identified in parentheses by country of publication):
this sort of thing: 90,278 newspapers (Australia 60,017, United States 30,261)
thing of this sort: 1,834 newspapers (Australia 1027, United States 807)
things of this sort: 1,557 newspapers (Australia 641, United States 916)
these sort of things: 1,437 newspapers (Australia 1,211, United States 226)
this sort of things: 331 newspapers (Australia 192, United States 139)
these sorts of things: 203 newspapers (Australia 142, United States 61)
these sort of thing: 23 newspapers (Australia 17, United States 6)
these sorts of thing: 1 newspaper (Australia 1, United States 0)
things of these sorts: 1 newspaper (Australia 1, United States 0)
this sorts of thing: 1 newspaper (Australia 1, United States 0)
this sorts of things: 1 newspaper (Australia 0, United States 1)
thing of these sort: none
thing of these sorts: none
things of these sort: none
thing of this sorts: none
things of this sorts: none
Clearly the dominant phrasing is "thing of this sort" at 90,278 matches, a figure that dwarfs two forms that I have heard used quite often and that (I believe) no one would be inclined to challenge as ungrammatical: "thing of this sort" (1,834) newspapers and "things of this sort" (1,557).
But then—to my surprise—comes the wording that the poster asks about—"these sort of things," at 1,437 matches. That number is not tremendously smaller than the numbers for "thing of this sort" and "things of this sort," and it leads me to believe that it is a (or was) a fairly common form of the expression in at least some part of the English-speaking world.
The most noticeable thing about the expression is how strongly the matches skew toward Australian sources: the ratio of Australian to U.S. sources is more than 5 to 1, as against slightly less than 3 to 1 for "thing of this sort," a bit more than 2 to 1 for "thing of this sort," and less than 1 to 1 for "things of this sort."
This last ratio is especially surprising, since one might expect that "this sort of things" might make a natural pairing with "things of this sort." But U.S. usage seems to accept "things of this sort" far more readily than it does "this sort of things."
Conclusion: Is 'these sort of things' grammatical?
If the test of grammaticality is usage, the Elephind search results tabulated above offer "these sort of things" some fairly impressive credentials for claiming legitimacy—at least in Australia, where, by a very thin margin, it is the second most common form in historical newspaper database occurrences after "this sort of thing." In the Elephind results from the United States, however, it finishes a less impressive fourth, and out-tallies the fifth-place "this sort of things" by a count of only 226 to 139.
As a practical matter, "this sort of thing" is the runaway winner in historical newspaper use in Australia and the United States. Both "thing of this sort" and "things of this sort" seem to pass the no-one-bats-an-eye test as well (at least, I've never heard anything against them), and that may be true of "these sort of things" in Australian usage, too. But in the United States that last wording is infrequent enough to prompt some degree of eye batting and perhaps even eyebrow raising when encountered unexpectedly.