I'll answer as I did find some kind of workaround
Those steps allow me to work DX-style with Managed Package, Namespace and Person Account
1 Create scratch org WITHOUT Namespace, using flag -n, --nonamespace
sfdx force:org:create -f config/project-scratch-def.json -a ScratchNONameSpace -s -n
2 First thing is to pull Account.Business_Account, which works as expected
$ sfdx force:source:status -r
=== Source Status
STATE FULL NAME TYPE PROJECT PATH
Remote Add Account.Business_Account RecordType
$ sfdx force:source:pull
=== Pulled SourceSTATE FULL NAME TYPE PROJECT PATH
Add Account.Business_Account RecordType force-app/main/default/objects/Account/recordTypes/Business_Account.recordType-meta.xml
3 Create scratch org WITH Namespace
sfdx force:org:create -f config/project-scratch-def.json -a ScratchWithNameSpace -s
4 Check status, you'll see conflicts
$ sfdx force:source:status
=== Source Status
STATE FULL NAME TYPE PROJECT PATH
Local Add (Conflict) Account.Business_Account RecordType force-app/main/default/objects/Account/recordTypes/Business_Account.recordType-meta.xml
Remote Changed (Conflict) Account.Business_Account RecordType force-app/main/default/objects/Account/recordTypes/Business_Account.recordType-meta.xml
5 Push your code using flag -f, --forceoverwrite
$ sfdx force:source:push -f
=== Pushed Source
STATE FULL NAME TYPE PROJECT PATH
Add Account.Business_Account RecordType force-app/main/default/objects/Account/recordTypes/Business_Account.recordType-meta.xml
$ sfdx force:source:status
=== Source Status
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After that you would be able to push/pull without issues.
Best Answer
The issue is because you are not pushing the profiles along with the other metadata. The FLS is present in the profiles . I usually recommend to move away from profiles and go with permission sets as those are more flexible .