I've checked with 1.10 and it's ok:
BUILD:  https://travis-ci.org/tarantool/tarantool/builds/458795680  
BRANCH:  https://github.com/tarantool/tarantool/tree/sergw/enable-parallel-test-replication-clean

I've also rebased on 2.1 and it's ok:
BUILD:  https://travis-ci.org/tarantool/tarantool/builds/459728459
BRANCH:  https://github.com/tarantool/tarantool/tree/sergw/enable-parallel-test-replication-clean-2.1

>Среда, 31 октября 2018, 21:28 +03:00 от Alexander Turenko < alexander.turenko@tarantool.org >:
>
>> >>I also observed a fail and a hang on box/:
>> >>
>> >> https://travis-ci.org/tarantool/tarantool/jobs/443475294#L2496
>> >> https://travis-ci.org/tarantool/tarantool/jobs/443475296#L6173
>> >>
>> >>Maybe test-run do something incorrect and the suites are not fully
>> >>independent in the parallel run? Maybe some tests from box/ and
>> >>replication/ conflicts on some global resource, say the same unix socket
>> >>name in /tmp?
>> >>
>> >>Please, try to reproduce the issue and fix / report it.
>> >
>> >Fixed problem with box/errinj (after adding new errinj, ordering of output 'box.error.injection.info()' changed) 
>>
>> Problem with engine/ddl is not depends on enabling replication tests in parallel mode.
>
>Please, file an issue re flaky test even if you do not have much details
>at the time.
>
>So it seems I have no more comments. Please, proceed with Vova.
>
>> >
>> >>
>> >>WBR, Alexander Turenko.
>> >>
>> >>On Sat, Oct 20, 2018 at 02:37:01AM +0300, Alexander Turenko wrote:
>> >>> It seems you catched segfault on the replication suite with this patch
>> >>> :)
>> >>> 
>> >>>  https://travis-ci.org/tarantool/tarantool/jobs/443475291#L2591
>
>To track: it was introduced in the patch and was fixed. See [1] for
>details.
>
>[1]:  https://github.com/tarantool/tarantool/issues/3765
>
>WBR, Alexander Turenko.


-- 
Sergei Voronezhskii