Mrdanga is not allowed inside Jagganatha Puri temple (they do not follow our rules, pancaratrica).

But Sri Bhakti-ratnakara 5.3128 states:

. In Sri Sangito-parijata it is said: "In the mRdaNga's middle part the demigod Brahma always resides. All the demigods who stay in Brahma's planet also stay in the mRdaNga. Because all the demigods reside within it, the mRdaNga is all auspicious." Music scholars say the mRdaNga and other musical instruments were created from the letters of the alphabet.

For us, since we would allow anyone in the temple, certainly even if mrdanga is contaminated (not Balarama mrdanga), we have to allow it. Haridasa Thakura never entered the Jagannatha Temple, nor did Rupa and Sanatana. The standard of external purity or not being contaminated by the killing of the cow is very high there:

kali-yuge sri krsna caitanya abatara
khelibara prabandhe kaila khola karatala

In the Kali-yuga Sri Krsna Caitanya descended to this world. He enjoyed kirtana pastimes with khola and karatala.

I have never found a confirmation to the suggestion that khola was actually designed by Mahaprabhu, but it is claimed. Leather is not the same as conch, don't mix up the two, conch is an acceptable item in the vedic temple, we are not vedic (vaidic) we are pancaratric.

The rule 'no animal skin in the temple' refers to any animal skin, regardless of the death (violent or natural).