From the perspective of Theravada, can a Mahayana follower attain Nibbana? And how about followers of other non-Theravadin Buddhisms? Why? If they cannot, what is the last stage of enlightenment that they are able to achieve?

Please refer to sources in your answers.
There aren't any texts within the Theravada school that talk about what happens to practitioners of other schools. The closest reference I can find in it is in the Mahaparinibbana Sutta, which says;


  Then Subhadda went to the Blessed One and exchanged courteous
  greetings with him. After an exchange of friendly greetings &amp;
  courtesies, he sat to one side. As he was sitting there, he said to
  the Blessed One, "Venerable sir, these brahmans &amp; contemplatives, each
  with his group, each with his community, each the teacher of his
  group, an honored leader, well-regarded by people at large — i.e.,
  Purana Kassapa, Makkhali Gosala, Ajita Kesakambalin, Pakudha
  Kaccayana, Sañjaya Belatthaputta, &amp; the Nigantha Nataputta: Do they
  all have direct knowledge as they themselves claim, or do they all not
  have direct knowledge, or do some of them have direct knowledge and
  some of them not?"
  
  "Enough, Subhadda. Put this question aside. I will teach you the
  Dhamma. Listen, and pay close attention. I will speak."
  
  "Yes, lord," Subhadda answered, and the Blessed One said, "In any
  doctrine &amp; discipline where the noble eightfold path is not found, no
  contemplative of the first... second... third... fourth order
  [stream-winner, once-returner, non-returner, or arahant] is found. But
  in any doctrine &amp; discipline where the noble eightfold path is found,
  contemplatives of the first... second... third... fourth order are
  found. The noble eightfold path is found in this doctrine &amp;
  discipline, and right here there are contemplatives of the first...
  second... third... fourth order. Other teachings are empty of
  knowledgeable contemplatives. And if the monks dwell rightly, this
  world will not be empty of arahants."
  http://www.accesstoinsight.org/tipitaka/dn/dn.16.5-6.than.html


Which I think indicates that as long as the Noble Eightfold Path is present, you can expect to find enlightened beings.

There is an additional issue of what happens with a person who makes a Bodhisattva vow. According to the Theravada school, a Bodhisattva must complete three great eons of practicing the ten Paramis in order to attain Buddhahood, but attaining stream entry, the first stage of enlightenment would cause that person to pass into parinibbana within seven lifetimes. As a result, a Bodhisattva will not attain stream entry or higher until the time when they are almost finished. If a Bodhisattva engages in vipassana meditation before that point, then they will be able to progress to Anulomanyana, the knowledge in which one sees the four noble truths, but the force of their Bodhisattva vow will stop them from going any further and accidentally attaining stream entry. This information is found in the commentary on the Majjhima Nikaya and is referenced in one of the Ven. Bhikkhu Bodhi's footnote on MN81 which says: 


  "MA notes that bodhisattas (or bodhisattvas in Sanskrit) go forth
  under the Buddhas to purify their virtue, learn the Buddha's
  teachings, practise the meditative life, and develop insight up to
  conformity knowledge (anulomanana). But they do not make effort to
  attain the paths and fruits (which would terminate their bodhisatta
  career)."