* Juncker says will fight for equal rights of east EU consumers
* But says "posted workers" reform will go ahead
* Juncker tells Warsaw, Budapest "rule of law is a must"
STRASBOURG, Sept 13 (Reuters) - European Commission chief Jean-Claude Juncker told the EU's eastern states on Wednesday he would fight for equal rights for their consumers, but their workers would not be allowed to unfairly undercut those in western members.
Juncker extended an olive branch to the eurosceptic governments in Poland, Hungary, Slovakia and the Czech Republic in his annual speech on the state of the European Union, where east-west divisions have driven a painful wedge.
"East to west: Europe must breathe with both lungs. Otherwise our continent will struggle for air," Junker said.
"In a union of equals, there can be no second class consumers. I will not accept that in some parts of Europe, people are sold food of lower quality than in other countries, despite the packaging and branding being identical."
Slovakia, the Czech Republic, Bulgaria and Romania have complained that food products sold by multinational producers on their markets are often of poorer quality than the same ones in the west.
Juncker said national authorities would be given better legal instruments to root out such "illegal practices", an attempt to woo the reluctant easterners at a time when the EU needs unity as it negotiates over the complex terms of Britain's departure in 2019.
In another gesture towards the eastern states, Juncker said it was time to let Bulgaria and Romania into the EU's Schengen zone of passport-free travel.
But he also said the bloc would go ahead with reforming its labour rules, which now allow workers from the poorer EU east to work in the wealthier west for low salaries.
French President Emmanuel Macron has made ending this practice, which he says amounts to social dumping, a key priority. The eastern states are opposed, saying they should be allowed to compete in that way to catch up after decades of communist rule after World War Two.
While the so-called "posted workers" only represent around one percent of the EU workforce, the issue has become sensitive.
EU diplomats say the bloc will change the current rules, a plan also backed by Belgium, the Netherlands and Luxembourg, in a move that could make it easier for Macron to carry out economic reforms at home by showing he is delivering for French workers.
"In a Union of equals, there can be no second class workers. Workers should earn the same pay for the same work in the same place," Juncker said, adding he would seek to establish an EU Labour Agency "for ensuring fairness in our single market."
RULE OF LAW
Juncker said he was "saddened" with the refusal by the ex-communist eastern states to take in refugees arriving in the bloc to help their western and southern peers.
More than two years of bruising battles over migration have caused a lot of bad blood in the EU, spilling over to other policy areas and reinforcing calls from the west to cut generous EU funding for the eastern states who deny help.
But Juncker reserved his most pointed criticism for Poland and Hungary, where nationalist governments have clashed with the Brussels on multiple issues, including a contested judiciary overhaul in Poland and Hungary's continued rejection of refugees despite the bloc's top court ruling that they must be taken in.
"The rule of law means that law and justice are upheld by an independent judiciary," Juncker said. "The judgements of the European Court of Justice have to be respected by all."
"To undermine them, or to undermine the independence of national courts, is to strip citizens of their fundamental rights. The rule of law is not optional in the European Union. It is a must."
As the EU contemplates deeper integration after Britain's departure, the eastern states - mostly outside the euro zone - fear they will be pushed out of the decision-making core and will lose out in a "multi-speed" EU.
Juncker offered some reassurances on that, saying he did not favour a separate euro zone budget, or a euro zone finance minister, but closer ties between all 27 EU states remaining after Brexit. (Reporting by Alastair Macdonald, Writing by Gabriela Baczynska; Editing by Mark Trevelyan)