ARP is an IPv4 protocol, and is unnecessary for IPv6. I don't see how even a bug would make it possible for IPv6 to rely on ARP. IPv6 and IPv4 are like ships in the night, they don't know about each other at all.
I've tried disabling ARP and I can't reproduce your problem between an RB750G and an RB433, both running 5.6. Here the devices:
[felix@rb433] > /system resource print
uptime: 19h5s
version: 5.6
free-memory: 49908KiB
total-memory: 62196KiB
cpu: MIPS 24Kc V7.4
cpu-count: 1
cpu-frequency: 300MHz
cpu-load: 1%
free-hdd-space: 29468KiB
total-hdd-space: 61440KiB
write-sect-since-reboot: 158
write-sect-total: 398070
bad-blocks: 0%
architecture-name: mipsbe
board-name: RB433
platform: MikroTik
[felix@rb750g] > /system resource print
uptime: 19h38s
version: 5.6
free-memory: 16588KiB
total-memory: 29708KiB
cpu: MIPS 24Kc V7.4
cpu-count: 1
cpu-frequency: 680MHz
cpu-load: 2%
free-hdd-space: 32072KiB
total-hdd-space: 61440KiB
write-sect-since-reboot: 1202
write-sect-total: 2224448
bad-blocks: 0%
architecture-name: mipsbe
board-name: RB750G
platform: MikroTik
I've turned off ARP on all the RB433 ethernet interfaces, as well as the RB750G interface that serves as the RB433 uplink:
[felix@rb433] > /interface ethernet print
Flags: X - disabled, R - running, S - slave
# NAME MTU MAC-ADDRESS ARP MASTER-PORT SWITCH
0 R 750 1500 00:0C:42:77:95:97 disabled
1 ether2 1500 00:0C:42:77:95:98 disabled none switch1
2 ether3 1500 00:0C:42:77:95:99 disabled none switch1
[felix@rb750g] > /interface ethernet print where name=433
Flags: X - disabled, R - running, S - slave
# NAME MTU MAC-ADDRESS ARP MASTER-PORT SWITCH
2 R 433 1500 00:0C:42:70:12:9A disabled none switch1
Here's an IPv6 address on a loopback on the 433:
[felix@rb433] > /ipv6 address print where interface=loopback0
Flags: X - disabled, I - invalid, D - dynamic, G - global, L - link-local
# ADDRESS INTERFACE ADVERTISE
0 G fd8a:ed9a:41f5:ffff::2/128 loopback0 no
I can ping that from the RB750G, as well as from a laptop behind a different port on the RB750G:
[felix@rb750g] > /ping fd8a:ed9a:41f5:ffff::2 count=4
HOST SIZE TTL TIME STATUS
fd8a:ed9a:41f5:ffff::2 56 64 0ms echo reply
fd8a:ed9a:41f5:ffff::2 56 64 0ms echo reply
fd8a:ed9a:41f5:ffff::2 56 64 0ms echo reply
fd8a:ed9a:41f5:ffff::2 56 64 0ms echo reply
sent=4 received=4 packet-loss=0% min-rtt=0ms avg-rtt=0ms max-rtt=0ms
HOST SIZE TTL TIME STATUS
$ ping6 -c 4 fd8a:ed9a:41f5:ffff::2
PING6(56=40+8+8 bytes) 2001:1938:2d2:1:b103:fc48:e2ae:c503 --> fd8a:ed9a:41f5:ffff::2
16 bytes from fd8a:ed9a:41f5:ffff::2, icmp_seq=0 hlim=63 time=1.643 ms
16 bytes from fd8a:ed9a:41f5:ffff::2, icmp_seq=1 hlim=63 time=1.686 ms
16 bytes from fd8a:ed9a:41f5:ffff::2, icmp_seq=2 hlim=63 time=1.735 ms
16 bytes from fd8a:ed9a:41f5:ffff::2, icmp_seq=3 hlim=63 time=1.765 ms
--- fd8a:ed9a:41f5:ffff::2 ping6 statistics ---
4 packets transmitted, 4 packets received, 0.0% packet loss
round-trip min/avg/max/std-dev = 1.643/1.707/1.765/0.047 ms
Granted, I didn't turn off ARP on ALL interfaces on the RB750G, but it's off on the RB433 completely (and IPv4 did stop working) as well as its uplink on the other side.
I did get interface flaps when changing ARP modes on the interfaces, it looks like the router tears down the interface on a PHY level, changes the setting, and then brings it back up. The logs show the interface going down and then back up, and the routing protocols between the two routes converging again. Is it possible that when you changed ARP modes for some reason the interfaces just stayed down on PHY and never came back up? Do you have console access to both routers to check interface status?