After the upanayana ritual, boys from the upper three varnas are able to receive knowledge from the Vedas. What about girls? Does this affect their karma?
Yes, females are allowed to read the Vedas. I am posting a passage from a famous 14th century text(Jivanmuktiviveka of Vidyaranya) which shows the importance of women Rishis in the formulation of the present day Hinduism and the equal rights enjoyed by women in Hinduism..
Renunciation is mentioned in the Taittiriya and other Upanishads: 'Some have attained immortality, not by acts, nor by offspring, nor by wealth, but by renunciation alone' (Kaivalya Upnaishad., 3). Females also are entitled to this kind of renunciation. The Caturdharike of the Mokshadharma, by using the word bhikshuki (female mendicant) with reference to the lady in question, when dealing with the controversy between Sulabha and janaka, indicated that females may renounce before marriage, or after the death of their husband and may go about as religious mendicants, may learn and hear the sastras dealing with moksha (namely the Upanishad and cognate literature), may meditate upon the atman in seclusion and assume the emblems of tri-danda, etc. In the wake of the argument in the Devatadhikarana (the section about devata) in the fourth chapter of the third book of the Sarirakabhasya, wherein a discussion has been started relating to the rights of a widower (to such renunciation), the name of the lady Vacaknavi has also been mentioned. These references go to strengthen the right claimed by Maitreyi, the wife of Yajnavalkya, of whom she inquires in the words: 'Of what use would such (wealth) be to me, if the possession of such would not render me immortal? Tell me whatever your worship knows,as to what I should do, in order to be free from mortality' (Brihadaranyaka Upanishad 4.5.4).
Jivanmuktiviveka of Vidyaranya translated by S. Subrahmanya Sastri and T.R. Srinivasa Ayangar, Chapter 1, Vividisa-samnyasa: The Renunciation of the Seeker
Women not barred from learning Vedas
Contrary to the popular belief that women are prohibited from learning the Vedas, here are two scholars who are on a mission to encourage women in mastering them. Speaking to The Hindu, Mysore-based Samveda Mahamandala President K.R. Manjunatha Shrouthy said not a single word was mentioned in the Vedas prohibiting woman from learning them.
“It is a misconception that reciting mantras from Vedas would affect child-bearing. In fact, there are some mantras like those found in Tandya Brahmana which should be recited by only women,” he pointed out.
Upapradhan Acharya of Acharyakulam (Haridwar) Krishna Bhatt taught the Rig Veda to his wife after their marriage.
“She did her Masters and M. Phil after marriage. She mastered the Vedas as well. I can proudly say that we are the only ghanapati [expert] couple in the entire country who recite Rig Veda,” he said.
Mr. Bhatt added that there were no restrictions on sudras acquiring divine knowledge. “At Acharyakulam, we are imparting Vedic knowledge to children of all prisms of life.
“All that they require is a qualification of Class V or VI in age group of 10 to 11,” he said. Dwelling on the Vedas and science, Mr. Shrouthy, a chartered accountant, said the Vedas referred to science and cited examples of gravitation theory and planetary movement.
“There are references to herbs for treatment of ailments in the Atharavana Veda. To unearth the essential aspects the Vedas and science, extensive research is the need of the hour, he added.