If you do not put the muscle/joint through its full ROM, then yes over time the muscle will shorten or become stiff. A muscle being short and a muscle being stiff are two different things - one is a length issue and the other is a tissue quality issue.
Do I feel that weightlifting will make you "stiff(er)"? If done improperly, maybe. But it wouldn't be the sole influencing factor. Your activities done outside of your training will factor into your "stiffness" much more than the weightlifting will. Sitting at a desk x 5-7 hours a day will cause your hips to become way more "stiff" than squatting or any other exercise.
When you weight train you cause micro trauma to the muscles so small bits of "scar tissue"/muscular adhesions can be created, so you can't just eliminate those from the equation since they commonly occur from weightlifting. Immediately after training, the muscles are full of blood, you get DOMS, etc which all can have a negative effect on ROM. Also, you take somebody who does bench 3x week without doing any pulling exercises and yes, their anterior shoulder muscles (pecs, etc) will become "stiff" due to the muscular imbalances being created.
So your loaded question of "can weightlifting make you stiff(er)?" with all of the extra circumstances (no joint issues, no injures, no stretching, etc) can best be answered like this: IMO, no. Weightlifting, if done properly, will not make you stiffer, as long as you are putting your joints through a full ROM. But again, your question and extra circumstances are poorly phrased and make it a loaded question.