Hello,

- I've downgraded Centos-7.7 to 7.6 and then 7.6 to 7.5 using "yum downgrade redhat-release" command by modifying "/etc/yum.repos.d/CentOS-Vault.repo" remo for respective version to downgrade.

Now downgrading from Centos-7.5 to 7.4, it is giving below conflicts error:

[vikrant@vikrant]# yum downgrade redhat-release
-------------------------
C7.4.1708-base
C7.4.1708-centosplus
C7.4.1708-extras
C7.4.1708-fasttrack
C7.4.1708-updates
-------------------------
-------------------------
-------------------------
Resolving Dependencies
--> Running transaction check
---> Package centos-release.x86_64 0:7-4.1708.el7.centos will be a downgrade
---> Package centos-release.x86_64 0:7-5.1804.el7.centos will be erased
--> Processing Conflict: initscripts-9.49.47-1.el7.x86_64 conflicts redhat-release < 7.5-0.11
--> Finished Dependency Resolution
Error: initscripts conflicts with centos-release-7-4.1708.el7.centos.x86_64
You could try using --skip-broken to work around the problem
You could try running: rpm -Va --nofiles --nodigest


- Not able to remove initscripts as many application depends on it

Sorry, but why are you doing this? While downgrading a package to avoid bugs introduced in a later version is nothing unusual, what are you trying to achieve by downgrading centos-release?

Especially to long UNsupported point-releases (7.4 is from 2017 and has been UNsupported since summer 2018, the OP needed the archive (vault.centos.org) site even to get to the outdated packages).
There are no real functional differences between the 7.x releases:
what doesn't work in 7.7/7.8 most likely didn't work in 7.4 either.

Removed initscripts
Same way downgraded successfully
Then installed initscripts for 7.4