It's strange, I cannot see anything "wrong" in you configuration (with or without DHCP server enabled).
The only thing I can see is the different L2 MTU 1598 vs. 1600, but no idea if it can affect anything, likely no.
You should ping without specifying the interface, however, the map should know itself which interface to choose.
Could it be an issue of some kind with the "auto" setting for bridge1 MAC?
In any case it is recommended to assign one manually, see Rule #6
Another thing, have you tried rebooting the map, after having made configuration changes?
Probably not what you want to hear, but at this point I would try an older, surely working version of RoS, 7.19.4 - even if proposed as "stable" - may have some issues.
Another thing I would try is a routing setup (as opposed to a bridge one).
Something like:
/interface bridge
add name=bridge1
/interface ethernet
set [ find default-name=ether1 ] comment=WAN
/interface wireless
set [ find default-name=wlan1 ] band=2ghz-b/g/n country=italy disabled=no mode=ap-bridge ssid=PedAP
/interface wireless security-profiles
set [ find default=yes ] supplicant-identity=MikroTik
/interface list
add comment=defconf name=WAN
add comment=defconf name=LAN
add comment=testconf name=LANandWAN include=LAN,WAN
/ip pool
add name=dhcp ranges=192.168.88.10-192.168.88.254
/ip dhcp-server
add address-pool=dhcp interface=wlan1 name=testconf
/ip address
add address=192.168.88.1/24 comment=testconf interface=wlan1 network=192.168.88.0
add address= 172.26.26.1/24 comment=testconf interface=ether1 network= 172.26.26.0
/interface list member
add comment=testconf interface=wlan1 list=LAN
add comment=testconf interface=ether1 list=WAN
/ip dhcp-server network
add address=192.168.88.0/24 comment=defconf dns-server=192.168.88.1 gateway=192.168.88.1 netmask=24
/ip firewall nat
add action=masquerade chain=srcnat comment="defconf: masquerade" ipsec-policy=out,none out-interface-list=WAN
/tool mac-server
set allowed-interface-list=LANandWAN
/tool mac-server mac-winbox
set allowed-interface-list=LANandWAN