"Modern" is not at all a word I would use to describe it. Authors like Esposito, Bellah, and Donner would like to suggest or focus on the egalitarian nature of the early Islamic community, because it makes people feel positively about inter-faith dialogue in the modern period. But we have to be very cautious about being anachronistic with our approach and our attitudes to a completely different people and time period. The early Islamic state was still a late antique/early medieval community, and with all the baggage that came along with that. Raiding and warfare were an everyday part of life. Forcing people to pay half of their possessions was seen as reasonable treatment for some locations during the Islamic conquests, for instance.

In terms of early Islamic institutions, the seventh century is categorized by the continued use of Byzantine and Sasanian law and administrative practices. The surviving evidence is making this clearer and clearer (Petra Sijpesteijn's brand new and very important Shaping a Muslim State discusses this). Seventh century CE Islamicate institutions weren't really groundbreaking from the administrative side at all, and it does seem it was fairly decentralized. Regional governors and their officials played a very important role in just how the state was run.

At the time, Islam could be described as fairly "progressive" in a great number of social issues, if this in particular is what you are interested in. Early Islamic treatment of women is a popular issue for this, where women were allowed a number of privileges and rights (both ownership of property and judicial rights, for instance) that their peers elsewhere didn't have. But this is still very far from anything we can consider "relatively modern."

In particular in the first two-three centuries of Islam, treatment of non-Muslim religious communities seems to have been much fairer than had occurred under the Byzantines and Sasanians, who had at times doctrinal/denominational disputes that led some religious groups to suffer. Both in the rights that they had, the level of tax they paid, and the protection and benefits that they received in exchange. Under the early Muslim community, there was a formative period where being "Muslim" (a religious identifier) and being "Arab" (an ethnic identifier) hadn't yet been completely separated, and we can see from early sources - in particular judicial ones - that the Muslims likely didn't really push conversion on early communities because many felt that Islam was a religion for Arabs and not non-Arabs. This, of course, would change, but it wasn't so clear-cut early on. (It also wasn't the only reason why conversion wasn't promoted, either, but I won't go too far into that here). It wasn't simply because they put forward ideas like "everyone should worship however they want without repercussions!" That wasn't the reality. There were practical reasons why they didn't promote conversion for so long, too.

If you'd like to read more about this, checking out Robert Hoyland's Seeing Islam as Others Saw It is a brilliant and vital work for understanding seventh century Islam from the non-Muslim viewpoint, and includes a huge number of partial translations of sources from the period.