Martin Odegaard started on his return to Madrid following a loan spell at Sociedad, while Casemiro dropped to the bench with Rodrygo and Vinicius Junior also handed a start.
Madrid looked to open up the hosts with Odegaard in particular the main protagonists in this regard, but the home side managed to clear their lines quite effectively.
Another opening fell Madrid's way following the midway point when a floating ball by Rodrygo picked out Karim Benzema in a threatening area, but Aritz Elustondo cleared.
Los Blancos were almost caught out at the other end when good pressing from Betis led Alexander Isak through on goal, but Thibaut Courtois parried after rushing off his goal-line.
Imanol Alguacil's troops asked further questions following the break after Ander Barrenetxea volleyed Mikel Oyarzabal's chipping ball across the face of Courtois' goal.
Madrid revived their attacking threats following the 61st minute as Benzema looked to pick out the bottom corner from the area, but Sociedad goalkeeper Alex Remiro went down to parry.
New signing and veteran David Silva made his debut for Sociedad two minutes later following his high-profile arrival from Premier League side Manchester City.
Consecutive attempts from Toni Kroos moments off each other almost opened up the hosts, but the German international was unable to bring Remiro to work.
Both sides were devoid of clear chances as the match began to wind down, thus settling for a point apiece in San Sebastian.