The 'residency type' programs haven't merged. The application system has been unified, but the residency programs and accrediting bodies (ACGME for MD, AOA for DO) operate independently of each other.
Get your facts straight.
Noone cares about 'DO methodology'. It's archaic, obsolete even. No MD student in their right mind is interested in learning something additional that they would never use, on top of the massive infocoepia they are already expected to know.
This idea of DO discrimination exists because there is a substantively lower standard for admission to DO school, and that somewhat calls into question the standards to which DO students will be held, as well as the quality of their education.
DO's are not considered 100% equivalent to MD's. If you want to do an ACGME residency as a DO, your USMLE scores are usually expected to be higher than the MD students you are competing with for a spot in a given residency program.
The DO exists because some fool named A.T. Still convinced enough chumps that "the human body possesses all it needs to heal itself" - yeah right, lets talk about infliximab if thats the case. Because of this, an entire 'distinguished' profession from those earning the MD degree was established.
I apologize if it seems as if I am defaming the DO profession - I'm just stating facts, not saying this reflects my own opinions.
OP, the truth remains, that until DO schools up their standards for admission, they will likely continue to be looked down upon.
Yerpp.