I wish to share some thoughts with you. I do NOT claim to have the answer.
1. However brilliant you are, you can't know everything.
2. However brilliant you may be, you can't know everything.
-- L.G. Alexander in the Longman English Grammar. He tells us that #2 is more "formal."
3. In my OPINION, some people (especially Americans?) might not have any problems with "However brilliant you be, you can't know everything."
a. We are talking about the SUBJUNCTIVE, I believe.
4. IF I understand my books correctly, your sentence could be expressed in many ways:
a. And yet, however he may try, can a political philosopher really be entirely neutral?
b. And yet, however he tries, can a ...?
c. And yet, however he try, can a ...?
d. And yet, however hard he may try, can a ...?
e. And yet, however hard he tries, can a ...?
f. And yet, however hard he try, can a ...?
5. Personally, I feel the most confident and comfortable with sentence "d." (Although I think that "f" sounds the most elegant, for I very much like the sound of the subjunctive.)
6. As you know, the writer of your sentence was Mr. Hugh Trevor-Roper, the famous English historian. Of course, he knew his grammar. He apparently was most comfortable with "c." (Remember: sometimes native speakers choose a certain way to express themselves because of euphony -- a pleasant sound. Apparently "c" sounded nice to Mr. Trevor-Roper.)
7. If you feel more comfortable with "b" or "e," I believe that you would be in good company. That is, I believe that many native speakers in 2014 would agree with you.
Student or Learner