We will use notation like "CAAC" to denote the sitting arrangement "CSC-ART-ART-CSC"

Let's say the seats are numbered 1, 2, 3,..., 50. WLOG, let's say a CSC majors are sitting in seats #1 and #2 (this is only not possible if no two CSC majors sit next to each other, but the only such configuration is CACACA...., and it's irrelevant since every Arts majors has two CSC neighbours)

Suppose no person has two CSC majors as neighbours. Then if we see the configuration "CA", it continues as "CAA", since "CAC" is not allowed. There can also be no more than two CSC majors in a row, since "CCC" is not allowed. So for seats 1...25, the seating arrangement looks like [at most 2 C][at least 2 A][at most 2 C][at least 2 A]....

Pair up groups like so:

[at most 2 C][at least 2 A] [at most 2 C][at least 2 A] [at most 2 C][at least 2 A]......

Since there is an equal number of C's and A's, it has to be the case that the sequence is actually

CCAACCAACCAA.....

(since the only way for the numbers to be equal is for there to be two C's in every pair of groups and 2 A's in every group)

Seat #25 cannot seat C since then we'd have 3 C's in a row.

So the seating is CCAACCAACCAA....CCAA.

Therefore there is an even number of C's at the table (since they appear in pairs) and an even number of A's at the table. But 25 is odd. Contradiction.

Assuming that the arrangement is possible leads to a contradiction, so the arrangement where no one has two CSC neighbours is not possible.