If we publish all papers in MDPI SCI journals during PhD studies, is it good?. Can it create some problems in future post doc apply or to apply some jobs?. What are your opinions?. What advantages/disadvantages it has?.
As far as I know, MDPI is a reputable publisher, may not popular or prestigious like Elsevier, Wiley, Springer, and so on though. Reputation of a publisher may depend on a number of factors such as age of publisher, number of journals publish, publishing policy, number of journals indexed in leading A&I databases, and so on. As an author, if you worry about the prestige/reputation/popularity of the publishing house, then you have to decide whether publishing in a journal belongs to MDPI or go for any other journal publish by more reputed publisher, and it's your choice. However, before selecting the publisher, I would consider many other things. For example, scope of the target journal, its readership, reputation of the journal, its visibility, editorial board, access mode (open access, subscription-based, etc.) and other things inherent to the target journal, but not for the publisher. Then it comes to the publisher. This is the general procedure which I follow, yet may not applicable for someone else. Therefore, to conclude, if your papers most appropriate for journals published by MDPI (and also indexed by SCI), then I cannot understand your reason for looking for another publisher. However, if you prefer publishing with diverse range of publishers or looking for more reputed publisher, I hope it won't be difficult to find a similar journal even from another publisher. Finally, I hope that the name of the publisher you worked with will not cause serious impact on your future endeavours.
MDPI is nowadays a well-established publisher dedicated to peer reviewed open access journals. A substantial number of their journals are SCI or (E)SCI(E) indexed. Even more journals are Scopus indexed. Depending on the scope they are PubMed indexed as well. Additionally they seem to get their new journals indexed in serious services and databases quite rapid. So no problem to publish some of your work in journals of MDPI.
Regardless which publisher we talk about I tend to say that in general it is better to spread your publications over different publishers (subscription as well as open access journals of Elsevier, Springer Nature, Wiley, ACS publications etc. and exclusively open access journals of MDPI, PLOS journals, Frontiers, Hindawi etc.).
Advantages are a broader audience, better quarantee to maximize visibility, greater chance to get your work published in the best suitable journal in terms of the overlap between the focus of your own paper and the scope of the journal.