Kuwait is more progressive than other Gulf Arab countries. A country's conservativeness/liberalism is measured by political system, civil society organizations, constitutionalism, press freedom, legal system and so on. Kuwait is a semi-democratic country with a hybrid political system divided by an elected parliament and appointed government. Kuwait has the highest degree of constitutionalism in the Gulf region, so it has the strongest civil society in the GCC region. Kuwait has the most free press in the Middle East and Arab world. Kuwait's legal system is more secular than other Gulf countries because Kuwait doesn't have Sharia Law punishments (flogging, stoning, amputation, crucifixion, etc.) unlike the UAE, Qatar and KSA. But alcohol and nightclubs aren't legally permitted in Kuwait because the parliament banned it in the early 1980s. In the UAE, Bahrain, Qatar and Oman, they do have legal alcohol and nightclubs but the citizens in those countries are much more conservative than Kuwaitis. The other Gulf Arab countries are absolute monarchies and completely autocratic.
Kuwaiti people are more liberal and Westernized than other Gulf Arab citizens. Among Gulf Arabs, it is common knowledge that Kuwaitis are the most liberal citizens in the GCC. You're not a Gulf citizen so you probably won't understand the differences in these societies. Emiratis are actually much more conservative than Kuwaitis, this is evidenced by the fact 99.9% of Emirati women wear the abaya. Many Kuwaiti women do not wear the abaya, it's common and prevalent in Kuwait to see local women who do not wear abaya. Some Kuwaiti women wear tank tops in public in Kuwait, this is something you'll never see the local women do in other Gulf countries. It's rare in the other Gulf states to see local women who don't wear the abaya - 99.9% of the local women in the UAE, Qatar, Bahrain, Oman and Saudi Arabia wear the black abaya and black hijab.
Among the Gulf Arab countries, Kuwait has the following: * Highest percentage of citizens with Western university education abroad * Highest percentage of Westernized citizens * Highest percentage of local women who don't wear abaya + who work (female labour force participation) * Highest percentage of citizens dating. Lowest percentage of arranged marriages among citizens (arranged marriages are still common, but not as common as in other GCC countries) * Highest percentage of atheist and secular/irreligious citizens
Nonetheless, Kuwait is still a Muslim society. You'll see many women in Kuwait wearing the abaya and other traditional clothes. But the situation here (among citizens) is better than other Gulf countries.
Kuwait is less progressive than Lebanon, Turkey, Palestine and Jordan but Kuwait isn't less progressive than Iraq, Yemen, Syria and the GCC states.