Apparently, there are some Muslim scholars who have ruled that committing bestiality does not invalidate the Hajj or fasts. Is this true? If it is, then how come sexual intercourse between a married couple does invalidate these religious activities but bestiality does not?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

Your statement that “Some Muslim scholars have ruled that committing bestiality does not invalidate the hajj or fasts” is correct. Their reasoning was that committing bestiality does not render the doer liable to receive the hadd (corporal punishment) of zina (fornication/adultery). Rather, he becomes liable only to taʻzeer (i.e. discretionary punishment). In this sense, it resembles sexual activity short of penetration. Those who held that committing bestiality invalidates the hajj and fasting classified bestiality as intercourse because it involves penetration into an unlawful vagina.

Ibn Qudaamah wrote, “There is no difference between intercourse in the anus or vagina with a human being or an animal. This is the view adopted by Ash-Shaafiʻi and Abu Thawr. The other opinion in this regard is that bestiality does not invalidate the hajj. This is the view of Maalik and Abu Haneefah, because committing bestiality does not render the doer liable to receive the hadd. In this sense, bestiality resembles sexual activity that does not amount to intercourse (penetration).” [Al-Mughni]

As for fasting, An-Nawawi stated in his book Al-Majmoo’ that one of the opinions of the Shaafiʻis is that penetration into an animal (bestiality) does not invalidate fasting based on what was mentioned by Ibn Qudaamah with regards to hajj.

Thus, there are two different opinions in this regard. This matter is open for ijtihaad (scholarly reasoning), and the person who chooses either of the two different opinions is not criticized.

Allaah knows best.